Spin Chain Integrability as a Supersymmetric Gauge Duality

Xiang-Mao Ding; Ting Zhang

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arXiv · 2506.18662

Spin Chain Integrability as a Supersymmetric Gauge Duality

Xiang-Mao Ding·Ting Zhang

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Abstract

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 $\Omega$-deformation parameter $\epsilon$.

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Xiang-Mao Ding, Ting Zhang. 2025-06-23. Spin Chain Integrability as a Supersymmetric Gauge Duality. https://arxiv.org/abs/2506.18662

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