Bailey chain approach to 2d $\mathcal{N}=(0,2)$ dualities

TL;DR

We address a $2$-dimensional $\mathcal{N}=(0,2)$ duality by constructing a Bailey-tree framework to prove elliptic-genus identities for quiver gauge theories generated from a seed duality. Central to the method are the integral operator $M(t)_{z;x}$ and the shift operator $I(s)$ that produce Bailey pairs, with the composition law $M(s)M(t)=M(st)$ enabling iterative Bailey transformations. Applying the framework to explicit seed theories (Theory A: $SU(2)$ with four chirals; Theory B: a Pfaffian-type LG model) yields $q$-hypergeometric integral identities equating their elliptic genera, and their quiver descendants. The approach provides a systematic route to duality proofs in low-dimensional supersymmetric theories and reveals connections to knot invariants and Yang–Baxter-type structures, suggesting fruitful directions for generalizations and cross-disciplinary applications.

Abstract

We study a two-dimensional $\mathcal{N}=(0,2)$ supersymmetric duality and construct novel Bailey pairs for the associated elliptic genera. This framework provides a systematic method to establish the equivalence of the elliptic genera of quiver gauge theories generated via iterative applications of the seed duality.