$SL(2,\mathbb{Z})$ dualities of boundary conditions in Abelian M2-brane SCFTs

TL;DR

This paper explores $SL(2,bZ)$ dualities of boundary conditions in 3D supersymmetric theories from M2-branes ending on M5-branes, revealing new dualities and anomaly matchings in Abelian and Chern-Simons models.

Contribution

It introduces novel $SL(2,bZ)$ dualities for boundary conditions in Abelian M2-brane SCFTs, including boundary conditions breaking gauge groups and matching anomalies.

Findings

Matching of 't Hooft anomalies for dual boundary conditions

Equivalence of supersymmetric half-indices across dualities

Generalization to $bZ_k$ gauge theories

Abstract

We propose $SL(2,\mathbb{Z})$ dualities of supersymmetric boundary conditions in the three-dimensional supersymmetric field theories describing a semi-infinite M2-brane terminating on M5-branes. Specifically, we present dualities of boundary conditions for Abelian (quiver) ADHM theories and circular quiver Chern-Simons matter theories including the ABJM model. For the circular quiver Chern-Simons theories we take boundary conditions breaking a $U(1)_1 \times U(1)_{-1}$ gauge group to its diagonal subgroup which is decoupled. This can be generalized to break $U(1)_k \times U(1)_{-k}$, leaving a $\mathbb{Z}_k$ gauge theory. We find matching of the 't Hooft anomalies and supersymmetric half-indices for all the proposed dual boundary conditions.