I am Clinical Professor of Physics at New York University. I am Ph.D. in Physics and Ph.D. in Philosophy. Address: 726 Broadway, New York City, NY10003, USA
Estudiamos la influencia que las exposiciones del matemático inglés Charles Howard Hinton de la i... more Estudiamos la influencia que las exposiciones del matemático inglés Charles Howard Hinton de la idea de la cuarta dimensión tuvieron sobre la obra de Jorge Luis Borges. Argumentamos que el principal aporte de los trabajos de Hinton para Borges fue el llamado de atención sobre la compatibilidad entre la idea de una cuarta dimensión del espacio y la filosofía kantiana. Esta idea provee a la literatura fantástica de un recurso extraordinario del que Borges supo valerse en muchas oportunidades; en sus cuentos, en columnas en periódicos, en alguno de sus poemas, en sus selecciones de textos para colecciones, en prólogos y hasta en cartas a sus allegados. La clave para entender de qué manera Borges relacionaba la cuarta dimensión del espacio con la filosofía kantiana se encuentra en una intrigante fecha a la que el escritor argentino remite en uno de sus textos: 1768. Ese año, enmarcado dentro del llamado período precrítico de la biografía intelectual de Kant, y esto permite descubrir una diferencia esencial entre la forma en que Borges y Hinton asociaron la cuarta dimensión con el pensamiento de Kant: mientras Hinton dedicó sus esfuerzos a mostrar la compatibilidad entre la geometría tetradimensional y el idealismo trascendental, Borges reparó en las meditaciones del período precrítico sobre la relación entre la cuarta dimensión y los espejos. En otras palabras, Hinton atendió a la gnoseología de Kant mientas que Borges, a su metafísica.
por aparecer en Revista de Estudios Kantianos, 2024
Allgemeine Naturgeschichte und Theorie des Himmels [Historia natural universal y teoría de los ci... more Allgemeine Naturgeschichte und Theorie des Himmels [Historia natural universal y teoría de los cielos] es, no sólo una de las obras más maduras del período precrítico de la biografía intelectual de Kant, sino uno de los libros más importantes que el prodigio de Königsberg haya escrito en toda su vida. Lejos de agotarse en meditaciones cosmológicas y una paráfrasis cualitativa de la teoría newtoniana de la gravitación, Historia natural universal y teoría de los cielos incluye una teoría de para la extensión de la substancia, una metafísica de las leyes de la naturaleza, consideraciones sobre teología, sobre ética y, como sostendrán algunos, hasta sobre antropología. Aquí, ofrecemos una lectura original de Historia natural universal y teoría de los cielos deteniéndonos en varios puntos cuya importancia ha pasado desapercibida en algunos comentarios de esta. Nuestro análisis hace foco en el contexto histórico-científico en que el libro de Kant fue escrito. La influencia que pensadores como Swedenborg y Wright tuvieron sobre Kant, y la estrecha relación que la teoría cosmológica de Kant guarda con las especulaciones de otros filósofos naturales de finales del siglo XVIII, como Michell y Laplace, permiten vislumbrar el panorama científico de su época: cuáles eran las preguntas de la filosofía natural y de la metafísica de las ciencias de la naturaleza en el momento en que Historia natural universal y teoría de los cielos fue terminado (1755). Asimismo, ofrecemos también una lectura de las intuiciones cosmológicas de Kant desde el punto de vista de la física actual.
The partition function of 3-dimensional quantum gravity has been argued to be 1-loop exact. Here,... more The partition function of 3-dimensional quantum gravity has been argued to be 1-loop exact. Here, we verify the vanishing of higher-orders in perturbation theory by explicit computation in the second-order, metric formulation at 3-loops. The number of 1-particle irreducible Feynman diagrams involving both gravitons and ghosts turns out to be 17. Using dimensional regularization, we solve all the diagrams. At 2-loops, we find that all such diagrams vanish separately after regularization. At 3-loops, in contrast, a series of remarkable cancellations between different diagrams takes place, with 9 diagrams beautifully conspiring to yield a vanishing result. Our techniques are suitable to be applied to higher loops as well as to similar computations in higher dimensions.
We give a novel definition of gravitational energy for an arbitrary theory of gravity including q... more We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein equations. We focus on the theory in four dimensions, in presence of negative cosmological constant, and with asymptotically anti-de Sitter (AdS) boundary conditions. As a first example, we compute the gravitational energy and angular momentum of Schwarzschild-AdS black holes, for which we obtain results consistent with previous computations performed using different methods. However, our method differs qualitatively from other ones in the feature of being intrinsically non-linear. It relies on the idea of adding to the gravity action topological invariant terms which suffice to regularize the Noether charges and render the variational problem well-posed. This is an idea that has been previously considered in the case of second-order theories, such as general relativity and which, as shown here, extends to higher-derivative theories. Besides black holes, we consider other solutions, such as gravitational waves in AdS, for which we also find results in agreement. This enables us to investigate the consistency of this approach in the non-Einstein sector of the theory.
Correspondencia en anticipación a La pregunta por la técnica. Correspondence in anticipation of T... more Correspondencia en anticipación a La pregunta por la técnica. Correspondence in anticipation of The question concernig technology.
Recibido el 26 de octubre de 2004; aceptado el 7 de diciembre de 2004 Esta breve nota tiene el fi... more Recibido el 26 de octubre de 2004; aceptado el 7 de diciembre de 2004 Esta breve nota tiene el fin didáctico de discutir el significado del principio de incertidumbre entre tiempo y energía en la mecánica cuántica en el contexto de los trabajos seminales sobre este tema. Eséste un aspecto que, a nuestro parecer, es ciertamente descuidado en muchos libros de texto. Así, estas páginas están pensadas para los estudiantes de un curso avanzado de mecánica cuántica y tienen la intención original de presentar una lista de referencias de los puntos que conforman las discusiones principales al respecto y pasar revista de las posibles interpretaciones. Discutimos también algunas de las falacias que, de manera recurrente, suelen relacionarse con la desigualdad de Heisenberg. Esta nota fue escrita para los alumnos del curso sobre mecánica cuántica dictado en la
Fil: Giribet, Gaston Enrique. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro ... more Fil: Giribet, Gaston Enrique. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Bahia Blanca. Instituto de Fisica del Sur; Argentina; Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina;
We consider string-inspired models in D ¼ 10 spacetime dimensions, which include couplings with 1... more We consider string-inspired models in D ¼ 10 spacetime dimensions, which include couplings with 1-and 3-form fields as well as R 4 higher-curvature corrections to the gravitational action. For such models, we explicitly construct a family of black hole solutions with both electric and magnetic charges, and with different horizon topologies. The solutions exhibit some features similar to those of self-gravitating monopoles in Einstein-Yang-Mills theory, which we discuss. When higher-curvature corrections are switched off, our solutions reduce to charged p-brane solutions previously studied in the literature. Novel qualitative features appear due to the R 4 terms, though. Such is the case for the emergence of branch singularities for charged solutions that, nonetheless, can be shielded by the event horizon.
We demonstrate that the near horizon symmetries of black holes in Einstein-Yang-Mills (EYM) theor... more We demonstrate that the near horizon symmetries of black holes in Einstein-Yang-Mills (EYM) theory are generated by an infinite-dimensional algebra that contains, in addition to supertranslations and superrotations, a non-Abelian loop algebra. This means that the Virasoro-Kac-Moody structure of EYM in asymptotically flat spacetimes has an exact analog in the near horizon region.
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We sta... more We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n − 2 winding modes actually coincide with the correlation functions in the SL(2, R)/U(1) gauged WZW model that include n − 2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference [1]. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.
We study n-string scattering amplitudes in three-dimensional Anti-de Sitter space (AdS 3). We foc... more We study n-string scattering amplitudes in three-dimensional Anti-de Sitter space (AdS 3). We focus our attention on the processes in which the winding number conservation is violated maximally; that is, those processes in which it is violated in n − 2 units. A worldsheet conformal field theory calculation leads us to confirm a previous conjecture about the functional form of these observables.
Besides black holes, the phase space of three-dimensional massive gravity about Warped Anti-de Si... more Besides black holes, the phase space of three-dimensional massive gravity about Warped Anti-de Sitter (WAdS) space contains solutions that decay exponentially in time. They describe evanescent graviton configurations that, while governed by a wave equation with non-vanishing effective mass, do not carry net gravitational energy. Explicit examples of such solutions have been found in the case of Topologically Massive Gravity; here, we generalize them to a much more general ghost-free massive deformation, with the difference being that the decay rate gets corrected due to the presence of higher-order terms.
We investigate symmetry breaking in two-dimensional field theories which have a holographic gravi... more We investigate symmetry breaking in two-dimensional field theories which have a holographic gravity dual. Being at large N , the Coleman theorem does not hold and Goldstone bosons are expected. We consider the minimal setup to describe a conserved current and a charged operator, and we perform holographic renormalization in order to find the correct Ward identities describing symmetry breaking. This involves some subtleties related to the different boundary conditions that a vector can have in the three-dimensional bulk. We establish which is the correct prescription that yields, after renormalization, the same Ward identities as in higher dimensions.
Einstein-Maxwell theory conformally coupled to a scalar field in D dimensions may exhibit a phase... more Einstein-Maxwell theory conformally coupled to a scalar field in D dimensions may exhibit a phase transition type instability at low temperature. We find an explicit solution that represents a charged asymptotically Anti-de Sitter black hole with a scalar field profile that is regular everywhere outside and on the horizon. This provides a tractable model to study the phase transition of hairy black holes in Anti-de Sitter space in which the backreaction on the geometry can be solved analytically. * mario-at-df.uba.ar † gaston-at-df.uba.ar ‡ af.goya-at-df.uba.ar § julioolivazapata-at-gmail.com
A solvable irrelevant deformation of AdS 3 /CFT 2 correspondence leading to a theory with Hagedor... more A solvable irrelevant deformation of AdS 3 /CFT 2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable TT deformations of two-dimensional CFTs. Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS 3 in the IR and a linear dilaton vacuum of little string theory in the UV. The insertion of the operator that realizes the deformation in the correlation functions produces a logarithmic divergence, leading to the renormalization of the primary operators, which thus acquire an anomalous dimension. We compute this anomalous dimension explicitly, and this provides us with a direct way of determining the spectrum of the theory. We discuss this and other features of the correlation functions in presence of the deformation.
I revisit the calculation of infinite-dimensional symmetries that emerge in the vicinity of isola... more I revisit the calculation of infinite-dimensional symmetries that emerge in the vicinity of isolated horizons. I focus the attention on extremal black holes, for which the isometry algebra that preserves a sensible set of asymptotic boundary conditions at the horizon strictly includes the BMS algebra. The conserved charges that correspond to this BMS sector, however, reduce to those of superrotation, generating only two copies of Witt algebra. For more general horizon isometries, in contrast, the charge algebra does include both Witt and supertranslations, being similar to BMS but s.str. differing from it. This work has been prepared for the proceedings of the XXII Simposio Sofichi 2020, held in Chile in November 2020. The material herein is based on my work in collaboration with Laura Donnay, Hernán González and Miguel Pino, and it is included in [1, 2].
This brief note has the didactical purpose of discussing the meaning of the uncertainty principle... more This brief note has the didactical purpose of discussing the meaning of the uncertainty principle involving energy and time in quantum mechanics by means of a review of the seminal works on this subject. The importance of this topic is, indeed, frequently neglected in several textbooks on quantum mechanics. Then, these pages are addressed to students attenting to an undergraduate course on quantum theory; and the original aim is that of presenting a list of references of the points that take part in the principal discussions on the subject. Special attention is devoted to the discussion of the fallacies, which are certainly persistent in the didactical literature.
We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N = 2... more We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N = 2 SCFT. We focus our attention on the SU(2) theory with N f = 4 flavor symmetry, whose partition function, according to AGT, is given by the Liouville four-point function on the sphere. The gauge theory with N f = 4 is known to exhibit SO(8) symmetry. We explain how the Weyl symmetry transformations of SO(8) flavor symmetry are realized in the Liouville theory picture. This is associated to functional properties of the Liouville four-point function that are a priori unexpected. In turn, this can be thought of as a non-trivial consistency check of AGT conjecture. We also make some comments on elementary surface operators and WZW theory.
Estudiamos la influencia que las exposiciones del matemático inglés Charles Howard Hinton de la i... more Estudiamos la influencia que las exposiciones del matemático inglés Charles Howard Hinton de la idea de la cuarta dimensión tuvieron sobre la obra de Jorge Luis Borges. Argumentamos que el principal aporte de los trabajos de Hinton para Borges fue el llamado de atención sobre la compatibilidad entre la idea de una cuarta dimensión del espacio y la filosofía kantiana. Esta idea provee a la literatura fantástica de un recurso extraordinario del que Borges supo valerse en muchas oportunidades; en sus cuentos, en columnas en periódicos, en alguno de sus poemas, en sus selecciones de textos para colecciones, en prólogos y hasta en cartas a sus allegados. La clave para entender de qué manera Borges relacionaba la cuarta dimensión del espacio con la filosofía kantiana se encuentra en una intrigante fecha a la que el escritor argentino remite en uno de sus textos: 1768. Ese año, enmarcado dentro del llamado período precrítico de la biografía intelectual de Kant, y esto permite descubrir una diferencia esencial entre la forma en que Borges y Hinton asociaron la cuarta dimensión con el pensamiento de Kant: mientras Hinton dedicó sus esfuerzos a mostrar la compatibilidad entre la geometría tetradimensional y el idealismo trascendental, Borges reparó en las meditaciones del período precrítico sobre la relación entre la cuarta dimensión y los espejos. En otras palabras, Hinton atendió a la gnoseología de Kant mientas que Borges, a su metafísica.
por aparecer en Revista de Estudios Kantianos, 2024
Allgemeine Naturgeschichte und Theorie des Himmels [Historia natural universal y teoría de los ci... more Allgemeine Naturgeschichte und Theorie des Himmels [Historia natural universal y teoría de los cielos] es, no sólo una de las obras más maduras del período precrítico de la biografía intelectual de Kant, sino uno de los libros más importantes que el prodigio de Königsberg haya escrito en toda su vida. Lejos de agotarse en meditaciones cosmológicas y una paráfrasis cualitativa de la teoría newtoniana de la gravitación, Historia natural universal y teoría de los cielos incluye una teoría de para la extensión de la substancia, una metafísica de las leyes de la naturaleza, consideraciones sobre teología, sobre ética y, como sostendrán algunos, hasta sobre antropología. Aquí, ofrecemos una lectura original de Historia natural universal y teoría de los cielos deteniéndonos en varios puntos cuya importancia ha pasado desapercibida en algunos comentarios de esta. Nuestro análisis hace foco en el contexto histórico-científico en que el libro de Kant fue escrito. La influencia que pensadores como Swedenborg y Wright tuvieron sobre Kant, y la estrecha relación que la teoría cosmológica de Kant guarda con las especulaciones de otros filósofos naturales de finales del siglo XVIII, como Michell y Laplace, permiten vislumbrar el panorama científico de su época: cuáles eran las preguntas de la filosofía natural y de la metafísica de las ciencias de la naturaleza en el momento en que Historia natural universal y teoría de los cielos fue terminado (1755). Asimismo, ofrecemos también una lectura de las intuiciones cosmológicas de Kant desde el punto de vista de la física actual.
The partition function of 3-dimensional quantum gravity has been argued to be 1-loop exact. Here,... more The partition function of 3-dimensional quantum gravity has been argued to be 1-loop exact. Here, we verify the vanishing of higher-orders in perturbation theory by explicit computation in the second-order, metric formulation at 3-loops. The number of 1-particle irreducible Feynman diagrams involving both gravitons and ghosts turns out to be 17. Using dimensional regularization, we solve all the diagrams. At 2-loops, we find that all such diagrams vanish separately after regularization. At 3-loops, in contrast, a series of remarkable cancellations between different diagrams takes place, with 9 diagrams beautifully conspiring to yield a vanishing result. Our techniques are suitable to be applied to higher loops as well as to similar computations in higher dimensions.
We give a novel definition of gravitational energy for an arbitrary theory of gravity including q... more We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein equations. We focus on the theory in four dimensions, in presence of negative cosmological constant, and with asymptotically anti-de Sitter (AdS) boundary conditions. As a first example, we compute the gravitational energy and angular momentum of Schwarzschild-AdS black holes, for which we obtain results consistent with previous computations performed using different methods. However, our method differs qualitatively from other ones in the feature of being intrinsically non-linear. It relies on the idea of adding to the gravity action topological invariant terms which suffice to regularize the Noether charges and render the variational problem well-posed. This is an idea that has been previously considered in the case of second-order theories, such as general relativity and which, as shown here, extends to higher-derivative theories. Besides black holes, we consider other solutions, such as gravitational waves in AdS, for which we also find results in agreement. This enables us to investigate the consistency of this approach in the non-Einstein sector of the theory.
Correspondencia en anticipación a La pregunta por la técnica. Correspondence in anticipation of T... more Correspondencia en anticipación a La pregunta por la técnica. Correspondence in anticipation of The question concernig technology.
Recibido el 26 de octubre de 2004; aceptado el 7 de diciembre de 2004 Esta breve nota tiene el fi... more Recibido el 26 de octubre de 2004; aceptado el 7 de diciembre de 2004 Esta breve nota tiene el fin didáctico de discutir el significado del principio de incertidumbre entre tiempo y energía en la mecánica cuántica en el contexto de los trabajos seminales sobre este tema. Eséste un aspecto que, a nuestro parecer, es ciertamente descuidado en muchos libros de texto. Así, estas páginas están pensadas para los estudiantes de un curso avanzado de mecánica cuántica y tienen la intención original de presentar una lista de referencias de los puntos que conforman las discusiones principales al respecto y pasar revista de las posibles interpretaciones. Discutimos también algunas de las falacias que, de manera recurrente, suelen relacionarse con la desigualdad de Heisenberg. Esta nota fue escrita para los alumnos del curso sobre mecánica cuántica dictado en la
Fil: Giribet, Gaston Enrique. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro ... more Fil: Giribet, Gaston Enrique. Consejo Nacional de Investigaciones Cientificas y Tecnicas. Centro Cientifico Tecnologico Bahia Blanca. Instituto de Fisica del Sur; Argentina; Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina;
We consider string-inspired models in D ¼ 10 spacetime dimensions, which include couplings with 1... more We consider string-inspired models in D ¼ 10 spacetime dimensions, which include couplings with 1-and 3-form fields as well as R 4 higher-curvature corrections to the gravitational action. For such models, we explicitly construct a family of black hole solutions with both electric and magnetic charges, and with different horizon topologies. The solutions exhibit some features similar to those of self-gravitating monopoles in Einstein-Yang-Mills theory, which we discuss. When higher-curvature corrections are switched off, our solutions reduce to charged p-brane solutions previously studied in the literature. Novel qualitative features appear due to the R 4 terms, though. Such is the case for the emergence of branch singularities for charged solutions that, nonetheless, can be shielded by the event horizon.
We demonstrate that the near horizon symmetries of black holes in Einstein-Yang-Mills (EYM) theor... more We demonstrate that the near horizon symmetries of black holes in Einstein-Yang-Mills (EYM) theory are generated by an infinite-dimensional algebra that contains, in addition to supertranslations and superrotations, a non-Abelian loop algebra. This means that the Virasoro-Kac-Moody structure of EYM in asymptotically flat spacetimes has an exact analog in the near horizon region.
We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We sta... more We study scattering amplitudes in two-dimensional string theory on a black hole bakground. We start with a simple derivation of the Fateev-Zamolodchikov-Zamolodchikov (FZZ) duality, which associates correlation functions of the sine-Liouville integrable model on the Riemann sphere to tree-level string amplitudes on the Euclidean two-dimensional black hole. This derivation of FZZ duality is based on perturbation theory, and it relies on a trick originally due to Fateev, which involves duality relations between different Selberg type integrals. This enables us to rewrite the correlation functions of sine-Liouville theory in terms of a special set of correlators in the gauged Wess-Zumino-Witten (WZW) theory, and use this to perform further consistency checks of the recently conjectured Generalized FZZ (GFZZ) duality. In particular, we prove that n-point correlation functions in sine-Liouville theory involving n − 2 winding modes actually coincide with the correlation functions in the SL(2, R)/U(1) gauged WZW model that include n − 2 oscillator operators of the type described by Giveon, Itzhaki and Kutasov in reference [1]. This proves the GFZZ duality for the case of tree level maximally winding violating n-point amplitudes with arbitrary n. We also comment on the connection between GFZZ and other marginal deformations previously considered in the literature.
We study n-string scattering amplitudes in three-dimensional Anti-de Sitter space (AdS 3). We foc... more We study n-string scattering amplitudes in three-dimensional Anti-de Sitter space (AdS 3). We focus our attention on the processes in which the winding number conservation is violated maximally; that is, those processes in which it is violated in n − 2 units. A worldsheet conformal field theory calculation leads us to confirm a previous conjecture about the functional form of these observables.
Besides black holes, the phase space of three-dimensional massive gravity about Warped Anti-de Si... more Besides black holes, the phase space of three-dimensional massive gravity about Warped Anti-de Sitter (WAdS) space contains solutions that decay exponentially in time. They describe evanescent graviton configurations that, while governed by a wave equation with non-vanishing effective mass, do not carry net gravitational energy. Explicit examples of such solutions have been found in the case of Topologically Massive Gravity; here, we generalize them to a much more general ghost-free massive deformation, with the difference being that the decay rate gets corrected due to the presence of higher-order terms.
We investigate symmetry breaking in two-dimensional field theories which have a holographic gravi... more We investigate symmetry breaking in two-dimensional field theories which have a holographic gravity dual. Being at large N , the Coleman theorem does not hold and Goldstone bosons are expected. We consider the minimal setup to describe a conserved current and a charged operator, and we perform holographic renormalization in order to find the correct Ward identities describing symmetry breaking. This involves some subtleties related to the different boundary conditions that a vector can have in the three-dimensional bulk. We establish which is the correct prescription that yields, after renormalization, the same Ward identities as in higher dimensions.
Einstein-Maxwell theory conformally coupled to a scalar field in D dimensions may exhibit a phase... more Einstein-Maxwell theory conformally coupled to a scalar field in D dimensions may exhibit a phase transition type instability at low temperature. We find an explicit solution that represents a charged asymptotically Anti-de Sitter black hole with a scalar field profile that is regular everywhere outside and on the horizon. This provides a tractable model to study the phase transition of hairy black holes in Anti-de Sitter space in which the backreaction on the geometry can be solved analytically. * mario-at-df.uba.ar † gaston-at-df.uba.ar ‡ af.goya-at-df.uba.ar § julioolivazapata-at-gmail.com
A solvable irrelevant deformation of AdS 3 /CFT 2 correspondence leading to a theory with Hagedor... more A solvable irrelevant deformation of AdS 3 /CFT 2 correspondence leading to a theory with Hagedorn spectrum at high energy has been recently proposed. It consists of a single trace deformation of the boundary theory, which is inspired by the recent work on solvable TT deformations of two-dimensional CFTs. Thought of as a worldsheet σ-model, the interpretation of the deformed theory from the bulk viewpoint is that of string theory on a background that interpolates between AdS 3 in the IR and a linear dilaton vacuum of little string theory in the UV. The insertion of the operator that realizes the deformation in the correlation functions produces a logarithmic divergence, leading to the renormalization of the primary operators, which thus acquire an anomalous dimension. We compute this anomalous dimension explicitly, and this provides us with a direct way of determining the spectrum of the theory. We discuss this and other features of the correlation functions in presence of the deformation.
I revisit the calculation of infinite-dimensional symmetries that emerge in the vicinity of isola... more I revisit the calculation of infinite-dimensional symmetries that emerge in the vicinity of isolated horizons. I focus the attention on extremal black holes, for which the isometry algebra that preserves a sensible set of asymptotic boundary conditions at the horizon strictly includes the BMS algebra. The conserved charges that correspond to this BMS sector, however, reduce to those of superrotation, generating only two copies of Witt algebra. For more general horizon isometries, in contrast, the charge algebra does include both Witt and supertranslations, being similar to BMS but s.str. differing from it. This work has been prepared for the proceedings of the XXII Simposio Sofichi 2020, held in Chile in November 2020. The material herein is based on my work in collaboration with Laura Donnay, Hernán González and Miguel Pino, and it is included in [1, 2].
This brief note has the didactical purpose of discussing the meaning of the uncertainty principle... more This brief note has the didactical purpose of discussing the meaning of the uncertainty principle involving energy and time in quantum mechanics by means of a review of the seminal works on this subject. The importance of this topic is, indeed, frequently neglected in several textbooks on quantum mechanics. Then, these pages are addressed to students attenting to an undergraduate course on quantum theory; and the original aim is that of presenting a list of references of the points that take part in the principal discussions on the subject. Special attention is devoted to the discussion of the fallacies, which are certainly persistent in the didactical literature.
We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N = 2... more We consider Alday-Gaiotto-Tachikawa (AGT) realization of the Nekrasov partition function of N = 2 SCFT. We focus our attention on the SU(2) theory with N f = 4 flavor symmetry, whose partition function, according to AGT, is given by the Liouville four-point function on the sphere. The gauge theory with N f = 4 is known to exhibit SO(8) symmetry. We explain how the Weyl symmetry transformations of SO(8) flavor symmetry are realized in the Liouville theory picture. This is associated to functional properties of the Liouville four-point function that are a priori unexpected. In turn, this can be thought of as a non-trivial consistency check of AGT conjecture. We also make some comments on elementary surface operators and WZW theory.
Analizamos el papel que desempeña la tridimensionalidad del espacio en la Crítica de la razón pur... more Analizamos el papel que desempeña la tridimensionalidad del espacio en la Crítica de la razón pura (KrV). Discutimos de qué manera la tridimensionalidad aparece en la estética trascendental, en la analítica de los conceptos y en la dialéctica trascendental. En particular, atendemos a los rasgos de continuidad que pueden reconocerse entre diferentes períodos del pensamiento kantiano en relación a cuestiones tales como la tridimensionalidad del espacio y su relación con la forma de afección de los objetos sobre nuestra mente.
Los agujeros negros, esos astros oscuros cuyo campo gravitacional le impide a la luz escapar de s... more Los agujeros negros, esos astros oscuros cuyo campo gravitacional le impide a la luz escapar de su interior sumiéndolos así en la más absoluta invisibilidad, son una férrea predicción de la teoría de la relatividad. Así lo advertía el físico alemán Karl Schwarzschild en la navidad de 1915. La teoría general de la relatividad, formulada por Albert Einstein en noviembre de 1915, nos lleva a repensar la interacción gravitatoria, ya no como una fuerza en el sentido newtoniano, sino en términos de la curvatura del espacio-tiempo mismo. Esta manera de entender la gravedad y el espacio-tiempo es la única en que nos es posible explicar la física que acaece en las inmediaciones de los agujeros negros, astros cuya existencia hemos confirmado en las últimas décadas de avances en la astrofísica. Aun así, hubo quienes, siglos antes de Einstein, tan solo asistidos por una intuición genial, habían ya especulado acerca de la existencia de enormes astros invisibles en el universo. La historia de esta oscura conjetura se remonta al siglo XVIII.
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