Star-triangle type relations from $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ dualities

Abstract

Inspired by the gauge/YBE correspondence this paper derives some star-triangle type relations from dualities in $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ supersymmetric quiver gauge theories. To be precise, we study two cases. The first case is the Intriligator-Pouliot duality in $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ theories. The description is performed explicitly for $N=1,2,3,4,5$ and also for $N=3k+2$, which generalizes the situation in $N=2,5$. For $N=1$ a triangle identity is obtained. For $N=2,5$ it is found that the realization of duality implies slight variations of a star-triangle relation type (STR type). The values $N=3,4$ are associated to a similar version of the asymmetric STR. The second case is a new duality for $2d$ $\mathcal{N}=(0,2)$ $USp(2N)$ theories with matter in the antisymmetric tensor representation that arises from dimensional reduction of $4d$ $\mathcal{N}=1$ $USp(2N)$ Csáki-Skiba-Schmaltz duality. It is shown that this duality is associated to a triangle type identity for any value of $N$. In all cases Boltzmann weights as well as interaction and normalization factors are completely determined. Finally, our relations are compared with those previously reported in the literature.

arXiv comment30 pages, no figures

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