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

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.