Quantum Spin Systems and Supersymmetric Gauge Theories, I
Norton Lee,Nikita Nekrasov +1 more
TLDR
In this article, the relation between supersymmetric gauge theories 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 periodic Toda chain.Abstract:
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.read more
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Conformal Bootstrap in Liouville Field Theory
TL;DR: In this article, Liouville Field Theory (LFT) was shown to reproduce some of the predictions of the matrix model approach, in particular the scaling behavior, genus one partition functions, and integrated correlation functions.
Journal ArticleDOI
Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
Abstract: We propose an interesting BPS/CFT correspondence playground: the correlation function of two intersecting half-BPS surface defects in four-dimensional $$ \mathcal{N} $$
= 2 supersymmetric SU(N) gauge theory with 2N fundamental hypermultiplets. We show it satisfies a difference equation, the fractional quantum T-Q relation. Its Fourier transform is the 5-point conformal block of the $$ {\hat{\mathfrak{sl}}}_N $$
current algebra with one of the vertex operators corresponding to the N-dimensional $$ {\mathfrak{sl}}_N $$
representation, which we demonstrate with the help of the Knizhnik-Zamolodchikov equation. We also identify the correlator with a state of the $$ {XXX}_{{\mathfrak{sl}}_2} $$
spin chain of N Heisenberg-Weyl modules over Y (
$$ {\mathfrak{sl}}_2 $$
). We discuss the associated quantum Lax operators, and connections to isomonodromic deformations.
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Exact WKB and the quantum Seiberg-Witten curve for 4d $N=2$ pure $SU(3)$ Yang-Mills, Part I: Abelianization
TL;DR: In this paper, the exact WKB method for the quantum Seiberg-Witten curve of 4d $N=2$ pure $SU(3)$ Yang-Mills, in the language of abelianization was investigated.
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Correlators on the wall and $\mathfrak{sl}_n$ spin chain
Mykola Dedushenko,Davide Gaiotto +1 more
TL;DR: In this paper, the authors studied the correlation functions of local operators at half-BPS interfaces engineered by the stacks of D5 or NS5 branes in the 4d $\mathcal{N}=4$ super Yang-Mills.
Posted Content
Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
TL;DR: In this paper, the correlation function of two intersecting half-BPS surface defects in four-dimensional supersymmetric $SU(N)$ gauge theory with $2N$ fundamental hypermultiplets is presented.
References
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TL;DR: In this article, the authors studied the vacuum structure and spectrum of N = 2 supersymmetric gauge theory in four dimensions, with gauge group SU(2), and obtained exact formulas for electron and dyon masses and the metric on the moduli space of vacua.
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Deformation Quantization of Poisson Manifolds
TL;DR: In this paper, it was shown that every finite-dimensional Poisson manifold X admits a canonical deformation quantization, and that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one correspondence with the class of Poisson structures on X modulo diffeomorphisms.
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Monopoles, duality and chiral symmetry breaking in N=2 supersymmetric QCD
TL;DR: In this article, the authors studied four dimensional N = 2 supersymmetric gauge theories with matter multiplets and derived the exact metric on the moduli space of quantum vacua and the exact spectrum of the stable massive states.
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Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
Nathan Seiberg,Edward Witten +1 more
TL;DR: In this paper, the vacuum structure and dyon spectrum of N = 2 supersymmetric gauge theory in four dimensions, with gauge group SU(2), were studied. And the theory turns out to have remarkably rich and physical properties which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and Dyon masses and the metric on the moduli space of vacua.
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Deformation quantization of Poisson manifolds, I
TL;DR: In this paper, it was shown that every finite-dimensional Poisson manifold X admits a canonical deformation quantization, which can be interpreted as correlators in topological open string theory.