3d Self-dualities

Keita Nii

doi:10.1016/j.nuclphysb.2019.03.017

Abstract

We investigate self-dualities in three-dimensional N=2 supersymmetric gauge theories. The electric and magnetic theories share the same gauge group. The examples include SU(2N), SO(7) and SO(8) gauge theories with various matter contents. In some examples, the duality exchanges the role of the baryon and Coulomb branch operators. In other examples, the Coulomb branch operator becomes an elementary field on the dual side. These self-dualities in turn teach us a correct quantum structure of the Coulomb moduli space of vacua. Some dualities exhibit symmetry enhancement.

Highlights

Duality is a very powerful tool of studying the low-energy dynamics of the strongly-coupled gauge theory
It is important to study the self-dualities because these examples sometimes exhibit symmetry enhancement in the farinfrared limit and because the symmetry enhancement is in turn related to the existence of many sets of dualities [5,6,7,8,9]
We investigate the possibility of the self-dualities in the 3d N = 2 supersymmetric gauge theories with various gauge groups and various matter contents

Summary

Introduction

Duality is a very powerful tool of studying the low-energy dynamics of the strongly-coupled gauge theory. We can construct the third self-dual description where the (anti-)baryonic operators and the Coulomb branch are introduced as elementary fields. We consider the self-duality in the 3d N = 2 SU(4) gauge theory with two anti-symmetric tensors and some (anti-)fundamental matters. The dual theory includes the gauge-singlet chiral superfields M0, M2, B1, B1, Y and Z as elementary fields These are identified with the moduli coordinates on the electric side. We denote the corresponding operator as Y bare Along this Coulomb branch, the massive components are integrated out and the mixed Chern-Simons term is induced between the two U(1) gauge groups keUf(f1)1U(2) = 2. B := Q4 B1 := AQ2 B1 := AQ2 Y bare := Y1Y2Y3 YAdressed := Y bareA YQdressed := Y bareQ2

First self-duality

Second self-duality

Third self-duality

Summary and Discussion