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

TL;DR

This paper derives star-triangle relations from dualities in 2D $ ext{N}=(0,2)$ USp(2N) supersymmetric theories, revealing new identities and generalizations linked to gauge/YBE correspondence.

Contribution

It introduces novel star-triangle type relations from 2D $ ext{N}=(0,2)$ USp(2N)$ dualities, including a new duality from dimensional reduction, with explicit formulas for various N values.

Findings

Derived explicit star-triangle relations for specific N values.

Identified a new duality related to antisymmetric matter in 2D theories.

Compared new relations with existing literature.

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 $4d$ $\mathcal{N}=1$ $USp(2N)$ Cs\'aki-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.