QCD3 dualities and the F-theorem

Adar Sharon

doi:10.1007/jhep08(2018)078

Abstract

There has recently been a surge of new ideas and results for 2+1 dimensional gauge theories. We consider a recently proposed duality for 2+1 dimensional QCD, which predicts a symmetry-breaking phase. Using the F-theorem, we find bounds on the range of parameters for which the symmetry-breaking phase (and the corresponding duality) can occur. We find exact bounds for an SU(2) gauge theory, and approximate bounds for an SU(N) gauge theory with N > 2.

Highlights

2.1 Phases of QCD3We quickly review the proposal in [1]
By tuning the deformations we introduce we can flow from SQCD3 to QCD3 such that the masses of the fermions m are small enough so that we are in the symmetry-breaking phase
We find here exactly the result we found in our numerical investigation - for large k and Nf, we cannot exclude a finite-sized symmetry-breaking window

Summary

Introduction

We quickly review the proposal in [1]. Consider an SU(N )k gauge theory coupled to Nf fermions in the fundamental representation in 2+1d (which we call QCD3). We adopt the notation in [1] for the Chern-Simons level, resulting in time reversal acting as k → −k in QCD3 Throughout this paper, k will always denote the QCD3 Chern-Simons level as defined above, while kwill denote the corresponding Chern-Simons level for SUSY theories. One could ask what are the low-energy phases of this theory as a function of the fermion masses m. It turns out that different phases appear in different regimes of the theory:

Objectives

Discussion

Conclusion