Defects at the Intersection: the Supergroup Side

Abstract

We consider two seemingly different theories in the Ω-background: one arises upon the most generic Higgsing of a 5d N = 1 U(N ) gauge theory coupled to matter, yielding a 3d-1d intersecting defect; the other one arises upon simple Higgsing of a 5d N = 1 U(N |M ) supergroup gauge theory coupled to super-matter, yielding another defect. The cases N = M = 1 are discussed in detail via equivariant localization to matrix-like models. The first theory exhibits itself a supergroup-like structure, which can be motivated via non-perturbative string dualities, and in a matter decoupling limit it is argued to be dual to a supergroup version of refined Chern-Simons theory. Furthermore, it is observed that the partition functions of the two defect theories are related by analytic continuation in one of the equivariant parameters. We find a common origin in the algebraic engineering through q-Virasoro screening currents. Another simple Higgsing of the 5d N = 1 U(1|1) yields a single component defect whose partition function is reminiscent of ordinary refined Chern-Simons on a lens space.

5d AGT correspondence of supergroup gauge theories from quantum toroidal $$ \mathfrak{gl} $$1

“…A generalization of the refined topological vertex [33][34][35][36] reproducing instanton partition functions called anti-refined topological vertex (anti-vertex) was as well proposed in [31]. Besides, relations with defects [37,38] and integrable systems [39] were also discussed previously. All of these previous studies imply the existence of an underlying algebraic structure in the belief of BPS/CFT correspondence.…”

“…See also[37,38], where a similar formula using two types of screening currents to reproduce partition functions of supergroup gauge theories was discussed.…”

5d AGT correspondence of supergroup gauge theories from quantum toroidal $\mathfrak{gl}_{1}$

“…A generalization of the refined topological vertex [34][35][36][37] reproducing instanton partition functions called anti-refined topological vertex (anti-vertex) was as well proposed in [32]. Besides, relations with defects [38,39] and integrable systems [40] were also discussed previously. All of these previous studies imply the existence of an underlying algebraic structure in the belief of BPS/CFT correspondence.…”

“…See also[38,39], where a similar formula using two types of screening currents to reproduce partition functions of supergroup gauge theories was discussed.…”