Spin Chain Integrability as a Supersymmetric Gauge Duality

Fuente: arXiv
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Main Authors: Ding, Xiang-Mao, Zhang, Ting
Format: Preprint
Published: 2025
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author Ding, Xiang-Mao
Zhang, Ting
author_facet Ding, Xiang-Mao
Zhang, Ting
contents We establish a novel correspondence between 4D $\mathcal N=1$ supersymmetric gauge theories on $D^2\times T^2$ and open XYZ spin chains with generalized boundary conditions, extending beyond previous 3D Bethe/gauge duality frameworks. Our primary contribution is the rigorous construction of the first exact duality between 4D BCD-type gauge theories and general-boundary XYZ spin chains governed by elliptic $R$-matrices. This framework provides a universal mechanism for resolving supersymmetric gauge theory/spin-chain duality across dimensional hierarchies: 2D $\mathcal{N}=(2,2)$ $\longleftrightarrow$ XXX spin chain, 3D $\mathcal{N}=2$ $\longleftrightarrow$ XXZ spin chain, 4D $\mathcal{N}=1$ $\longleftrightarrow$ XYZ spin chain, mediated through the $Ω$-deformation parameter $ε$.
format Preprint
id arxiv_https___arxiv_org_abs_2506_18662
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Spin Chain Integrability as a Supersymmetric Gauge Duality
Ding, Xiang-Mao
Zhang, Ting
High Energy Physics - Theory
Mathematical Physics
We establish a novel correspondence between 4D $\mathcal N=1$ supersymmetric gauge theories on $D^2\times T^2$ and open XYZ spin chains with generalized boundary conditions, extending beyond previous 3D Bethe/gauge duality frameworks. Our primary contribution is the rigorous construction of the first exact duality between 4D BCD-type gauge theories and general-boundary XYZ spin chains governed by elliptic $R$-matrices. This framework provides a universal mechanism for resolving supersymmetric gauge theory/spin-chain duality across dimensional hierarchies: 2D $\mathcal{N}=(2,2)$ $\longleftrightarrow$ XXX spin chain, 3D $\mathcal{N}=2$ $\longleftrightarrow$ XXZ spin chain, 4D $\mathcal{N}=1$ $\longleftrightarrow$ XYZ spin chain, mediated through the $Ω$-deformation parameter $ε$.
title Spin Chain Integrability as a Supersymmetric Gauge Duality
topic High Energy Physics - Theory
Mathematical Physics
url https://arxiv.org/abs/2506.18662