Quantum Spin Systems and Supersymmetric Gauge Theories, I

Fuente: arXiv
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Main Authors: Lee, Norton, Nekrasov, Nikita
Format: Preprint
Published: 2020
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author Lee, Norton
Nekrasov, Nikita
author_facet Lee, Norton
Nekrasov, Nikita
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2009_11199
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Quantum Spin Systems and Supersymmetric Gauge Theories, I
Lee, Norton
Nekrasov, Nikita
High Energy Physics - Theory
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.
title Quantum Spin Systems and Supersymmetric Gauge Theories, I
topic High Energy Physics - Theory
url https://arxiv.org/abs/2009.11199