Spin Chain Integrability as a Supersymmetric Gauge Duality
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915355825274880 |
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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 |
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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 |