Intersecting defects and supergroup gauge theory

Abstract

We consider 5d supersymmetric gauge theories with unitary groups in the Ωbackground 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 Ω-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.

Virasoro Constraint for Uglov Matrix Model

“…By considering these two screening currents at the same time, one can discuss the supergroup analog of the (q-)matrix model[KN21,CZ21].…”

On refined Chern–Simons and refined ABJ matrix models

“…The partition function of ABJ theory can be expressed as a matrix integral over two sets of independent variables {x i } N i=1 and {y a } M a=1 which can be interpreted as the eigenvalues of an Hermitean super-matrix in the Lie super-algebra of U (N |M). The usual Vandermonde determinant in the measure is first substituted by the Cauchy determinant and then q, t-deformed to the function (see [40][41][42])…”

Defects at the Intersection: the Supergroup Side

“…This note, a brief account of the results published in [17] (supplemented by original computations in Subsection 2.1), is about yet another place where supergroup gauge theories, a supergroup version of refined Chern-Simons in particular [18], show up: SUSY theories based on ordinary gauge groups but supported on intersecting subspaces embedded in an ambient space. The intersecting gauge theories of our interest arise upon Higgsing a parent 5d SUSY gauge theory with unitary group in the Ω-background C 2 q,t −1 × S 1 , while the support of the defects is given by the two orthogonal cigars C q × S 1 and C t −1 × S 1 intersecting at the origin along a common circle (Fig.…”

“…Let us note that, because of the original q ↔ t −1 symmetry, we considered here the chamber |q| < 1, |t −1 | < 1, which is, however, tricky for the unrefined limit. The case |q| < 1, |t| < 1 is discussed in[17].…”