Intersecting Defects and Supergroup Gauge Theory

TL;DR

This paper investigates intersecting BPS defects in 5d supersymmetric gauge theories, revealing dualities with supergroup gauge theories and connections to refined topological strings and super-instanton counting.

Contribution

It introduces a novel framework for intersecting defects via Higgsing, linking them to supergroup gauge theories and refined Chern-Simons theory through dualities and string theory embeddings.

Findings

Duality between intersecting defects and supergroup gauge theories.

Identification of supergroup refined Chern-Simons theory via topological string duality.

Large rank duality with super-instanton counting in BPS/CFT correspondence.

Abstract

We consider 5d supersymmetric gauge theories with unitary groups in the $\Omega$-background and study codim-2/4 BPS defects supported on orthogonal planes intersecting at the origin along a circle. The intersecting defects arise upon implementing the most generic Higgsing (geometric transition) to the parent higher dimensional theory, and they are described by pairs of 3d supersymmetric gauge theories with unitary groups interacting through 1d matter at the intersection. We explore the relations between instanton and generalized vortex calculus, pointing out a duality between intersecting defects subject to the $\Omega$-background and a deformation of supergroup gauge theories, the exact supergroup point being achieved in the self-dual or unrefined limit. Embedding our setup into refined topological strings and in the simplest case when the parent 5d theory is Abelian, we are able to identify the supergroup theory dual to the intersecting defects as the supergroup version of refined Chern-Simons theory via open/closed duality. We also discuss the BPS/CFT side of the correspondence, finding an interesting large rank duality with super-instanton counting.