Papers by Nikita Nekrasov
arXiv: High Energy Physics - Theory, 2020
The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is... more The relation between supersymmetric gauge theories in four dimensions and quantum spin systems is exploited to find an explicit formula for the Jost function of the $N$ site $\mathfrak{sl}_{2}$ $XXX$ spin chain (for infinite dimensional complex spin representations), as well as the $SL_N$ Gaudin system, which reduces, in a limiting case, to that of the $N$-particle periodic Toda chain. Using the non-perturbative Dyson-Schwinger equations of the supersymmetric gauge theory we establish relations between the spin chain commuting Hamiltonians with the twisted chiral ring of gauge theory. Along the way we explore the chamber dependence of the supersymmetric partition function, also the expectation value of the surface defects, giving new evidence for the AGT conjecture.
Ludwig Faddeev Memorial Volume, May 21, 2018
In quantizing classical mechanical systems one often sums over the classical trajectories as in l... more In quantizing classical mechanical systems one often sums over the classical trajectories as in localization formulas, but also takes into account the contributions of the "instanton gas": a set of approximate solutions of the equations of motion. This paper attempts to alleviate some of the frustrations of this 40+ years old approach by finding the honest solutions of equations of motion of the complexified classical mechanical system. These ideas originate in the Bethe/gauge correspondence. The examples include algebraic integrable systems, from the abstract Hitchin systems to the well-studied anharmonic oscillator. We also speculate on the applications to the black hole radiation. We elucidate the relation between Lefschetz thimbles and the Ω-deformed B-model. We propose the notion of the topological renormalization group.
Functional Analysis and Its Applications, 1994
ABSTRACT
Eprint Arxiv Hep Th 9909213, Sep 29, 1999
We propose an approximate wavefunction of the bound state of $N$ $D0$-branes. Its spread grows as... more We propose an approximate wavefunction of the bound state of $N$ $D0$-branes. Its spread grows as $N^{1\over 3}$ per particle, i.e. it saturates the Polchinski's bound.
We point out a map between the dynamics of a non-relativistic system of $N$ particles in one dime... more We point out a map between the dynamics of a non-relativistic system of $N$ particles in one dimension interacting via the pair-wise potentials $U_I(q) = (\nu^2/4R^2)\sin^2(q/2R)$ and the one of the particles with the pair potential $U_{II}(q) = \nu^2/q^2$ and the external potential $U_{ext} = \omega^2 q^2/2$. The natural relation between the frequency $\omega$ and the radius $R$ is: $\omega R = 1$.
The curved beta-gamma system is the chiral sector of a certain infinite radius limit of the non-l... more The curved beta-gamma system is the chiral sector of a certain infinite radius limit of the non-linear sigma model with complex target space. Naively it only depends on the complex structures on the worldsheet and the target space. It may suffer from the worldsheet and target space diffeomorphism anomalies. We analyze the curved beta-gamma system on the space of pure spinors, aiming to verify the consistency of Berkovits covariant superstring quantization. We demonstrate that under certain conditions both anomalies can be cancelled for the pure spinor sigma model, in which case one reproduces the old construction of B.Feigin and E.Frenkel.
Fortschritte Der Physik, 2000
Available from https://www3.interscience.wiley.com/cgi- bin/abstract/68501154/START
Eprint Arxiv 1312 6689, Dec 23, 2013
We study macroscopically two dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories constr... more We study macroscopically two dimensional $\mathcal{N}=(2,2)$ supersymmetric gauge theories constructed by compactifying the quiver gauge theories with eight supercharges on a product $\mathbb{T}^{d} \times \mathbb{R}^{2}_{\epsilon}$ of a $d$-dimensional torus and a two dimensional cigar with $\Omega$-deformation. We compute the universal part of the effective twisted superpotential. In doing so we establish the correspondence between the gauge theories, quantization of the moduli spaces of instantons on $\mathbb{R}^{2-d} \times \mathbb{T}^{2+d}$ and singular monopoles on $\mathbb{R}^{2-d} \times \mathbb{T}^{1+d}$, for $d=0,1,2$, and the Yangian $\mathbf{Y}_{\epsilon}(\mathfrak{g}_{\Gamma})$, quantum affine algebra $\mathbf{U}^{\mathrm{aff}}_q(\mathfrak{g}_{\Gamma})$, or the quantum elliptic algebra $\mathbf{U}^{\mathrm{ell}}_{q,p}(\mathfrak{g}_{\Gamma})$ associated to Kac-Moody algebra $\mathfrak{g}_{\Gamma}$ for quiver $\Gamma$.
Journal of High Energy Physics, 2016
AIP Conference Proceedings, 2006
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2001
In this almost non-technical note, mostly aimed at mathematicians, we review the construction of ... more In this almost non-technical note, mostly aimed at mathematicians, we review the construction of instantons on the non-commutative R 4 and explain how their existence is tied up with the existence of M -theory.
Nuclear Physics B - Proceedings Supplements, 2011
The moduli space of SL2 flat connections on a punctured Riemann surface Σ with the fixed conjugac... more The moduli space of SL2 flat connections on a punctured Riemann surface Σ with the fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates, in which the generating function of the variety of SL2-opers is identified with the universal part of the effective twisted superpotential of the Gaiotto type four dimensional N = 2 supersymmetric theory subject to the two-dimensional Ω-deformation. This allows to give a definition of the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group, and connect it to the instanton counting of the four dimensional gauge theories, in the rank one case.
Japanese Journal of Mathematics, 2009
Nuclear Physics B, 1997
We investigate higher-dimensional analogues of the bc systems of 2D RCFT. When coupled to gauge f... more We investigate higher-dimensional analogues of the bc systems of 2D RCFT. When coupled to gauge fields and Beltrami differentials defining integrable holomorphic structures, the bc partition functions can be explicitly evaluated using anomalies and holomorphy. The resulting induced actions generalize the chiral algebras of 2D RCFT to 2 n dimensions. Moreover, bc systems in four and six dimensions are closely related to supersymmetric matter. In particular, we show that d = 4, N = 2 hypermultiplets induce a theory of self-dual Yang-Mills fields coupled to self-dual gravity. In this way the bc systems fermionize both the algebraic sector of the WZW 4 theory, as defined by Losev et al., and the classical open NWS = 2 string.
Journal of High Energy Physics, Mar 16, 2004
In this paper we show how S-duality of type-IIB superstrings leads to an S-duality relating A- an... more In this paper we show how S-duality of type-IIB superstrings leads to an S-duality relating A- and B-model topological strings on the same Calabi-Yau as had been conjectured recently: D-instantons of the B-model correspond to A-model perturbative amplitudes and D-instantons of the A-model capture perturbative B-model amplitudes. Moreover this confirms the existence of new branes in the two models. As an application we explain the recent results concerning A-model topological strings on Calabi-Yau and its equivalence to the statistical mechanical model of melting crystal.
This paper lays groundwork for the detailed study of the non-trivial renormalization group flow c... more This paper lays groundwork for the detailed study of the non-trivial renormalization group flow connecting supersymmetric fixed points in four dimensions using string theory on AdS spaces. Specifically, we consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The N = 1 superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE N = 2 superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry with a single D3-brane and discuss the near-horizon supergravity solution for a large number N of coincident D3-branes. 3 On leave of absence from St. Petersburg Steklov Mathematical Institute 11/98
Nuclear Physics B, Jun 1, 1998
We introduce special supersymmetric gauge theories in three, five, seven and nine dimensions, who... more We introduce special supersymmetric gauge theories in three, five, seven and nine dimensions, whose compactification on two-, four-, six- and eight folds produces a supersymmetric quantum mechanics on moduli spaces of holomorphic bundles and/or solutions to the analogues of instanton equations in higher dimensions. The theories may occur on the world-volumes of D-branes wrapping manifolds of a special holonomy. We also discuss the theories with matter.
Letters in Mathematical Physics, 2005
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Papers by Nikita Nekrasov