Self-conjugate QCD

Mohamed M Anber

doi:10.1007/jhep10(2019)042

Abstract

We carry out a systematic study of SU(6) Yang-Mills theory endowed with fermions in the adjoint and 3-index antisymmetric mixed-representation. The fermion bilinear in the 3-index antisymmetric representation vanishes identically, which leads to interesting new phenomena. We first study the theory on a small circle, i.e., on {mathrm{mathbb{R}}}^3times {mathbbm{S}}_L^1 , employing symmetry-twisted boundary conditions and semi-classical techniques. We find that the ground state is 3-fold degenerate, which can be explained as a consequence of a 1-form/0-form mixed ’t Hooft anomaly. In addition, the theory may admit massless bosonic and fermionic degrees of freedom, depending on the number of flavors, and confines the electric probes in the infrared. Empowered by ’t Hooft anomaly matching conditions along with the 2-loop β-function, we further examine the possible infrared symmetry realizations on ℝ4 for various number of adjoint and 3-index antisymmetric fermions. The infrared theory is either a conformal field theory, which is expected for a large number of flavors, or it is confining with or without chiral symmetry breaking. In a few cases, we are able to give enough evidence for adiabatic continuity between the small- and large-circle limits.

Highlights

JHEP10(2019)042 to a cancelation among the excited states, retaining mainly the ground state of the system
We find that the ground state is 3-fold degenerate, which can be explained as a consequence of a 1form/0-form mixed ’t Hooft anomaly
In the absence of adjoint fermions we find that the discrete chiral symmetry is broken, the vacuum is 3-fold degenerate, the IR spectrum is fully gapped, and the theory confines the fundamental electric probes

Summary

Introduction

JHEP10(2019)042 to a cancelation among the excited states, retaining mainly the ground state of the system. With the aid of the 2-loop β-function, we employ ’t Hooft anomaly matching conditions to give a strong evidence that Yang-Mills theory with a single fermion in the 3-index antisymmetric representation is adiabatically continuous on R3 × S1L for all values of L, i.e., it does not experience a phase transition as we change the circle size. A theory with nR fermions (and no adjoints) will either flow to a strongly coupled confining regime (with or without symmetry breaking), if the β-function does not develop a fixed point, or to a CFT otherwise.

Objectives

Results

Conclusion