$$ \mathcal{N} = 2 $$ gauge theories on unoriented/open four-manifolds and their AGT counterparts

258

We develop new techniques for computing exact correlation functions of a class of local operators, including certain monopole operators, in three-dimensional N = 4 abelian gauge theories that have superconformal infrared limits. These operators are position-dependent linear combinations of Coulomb branch operators. They form a onedimensional topological sector that encodes a deformation quantization of the Coulomb branch chiral ring, and their correlation functions completely fix the (n ≤ 3)-point functions of all half-BPS Coulomb branch operators. Using these results, we provide new derivations of the conformal dimension of half-BPS monopole operators as well as new and detailed tests of mirror symmetry. Our main approach involves supersymmetric localization on a hemisphere HS 3 with half-BPS boundary conditions, where operator insertions within the hemisphere are represented by certain shift operators acting on the HS 3 wavefunction. By gluing a pair of such wavefunctions, we obtain correlators on S 3 with an arbitrary number of operator insertions. Finally, we show that our results can be recovered by dimensionally reducing the Schur index of 4D N = 2 theories decorated by BPS 't Hooft-Wilson loops.

Section: Discussionmentioning

confidence: 99%

Coulomb branch operators and mirror symmetry in three dimensions

Dedushenko

Fan

Pufu

et al. 2018

258

“…24) The N c = 1 case was discussed in [18]. The U(1) W=M + +M − theory with 4 flavors and 8 flipping fields appears as a boundary condition for N = 2 rank-1 class-S SCFT's [52]. The SU(4) 2 × U(1) global symmetry breaks to SU(3) 2 × U(1) × U(1), so the process removes one linear monopole superpotential term (if both monopole terms M + and M − were present, the new U(1) symmetry would be broken).…”

Section: U(n C ) With 4 Flavors W = M + + M −mentioning

confidence: 99%

A tale of exceptional 3d dualities

Benvenuti

2019

Self Cite

121

We consider interesting Seiberg dualities for Usp gauge theories with an antisymmetric, 8 fundamentals and no superpotential. We reduce to three dimensions and systematically analyze deformations triggered by real and complex masses, reaching a plethora of N = 2 dualities for U(N) and Usp(2N) gauge theories, possibly with monopole superpotentials and Chern-Simons interactions. Special cases of these "exceptional dualities" are: supersymmetry enhancement dualities, "duality appetizers" and many known dualities relating rank-1 gauge groups. The 4d N = 1 Usp dualities provide a unified perspective on many curious phenomena of 3d and 4d gauge theories with four supercharges. Finally, we propose a free mirror for A 2N Argyres-Douglas, with its related adjoint-Usp(2N) duality, and we construct a mirror for adjoint-U(N), with an arbitrary number flavors and zero superpotential.

“…Speaking more broadly, the general idea of gluing has appeared in multiple references on supersymmetric field theories, see e.g. [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47].…”

Section: What We Really Domentioning

confidence: 99%

Gluing. Part I. Integrals and symmetries

Dedushenko

2020

We review some aspects of the cutting and gluing law in local quantum field theory (QFT) and study it from a new point of view. In particular, we emphasize the description of gluing by a path integral over a space of polarized boundary conditions, which are given by leaves of some Lagrangian foliation in the phase space. We think of this path integral as a non-local (d − 1)-dimensional gluing theory associated to the parent local d-dimensional QFT. This is a novel point of view paving the way for applications of the standard QFT techniques (that do not rely on locality) to the gluing theory. We describe various properties of this procedure and spell out conditions under which symmetries of the parent theory lead to symmetries of the gluing theory. The purpose of this paper is to set up a playground for the companion paper where these techniques are applied to obtain new results in supersymmetric theories.