Higher Representations: Confinement and Large N

TL;DR

This paper studies the phase transition behavior in gauge theories with fermions in two index representations, analyzing the role of center symmetry and large N limits, with implications for understanding confinement and chiral symmetry.

Contribution

It extends the analysis of confinement phase transitions to theories with higher dimensional fermion representations and large N, highlighting differences from super Yang-Mills and exploring the role of center symmetry.

Findings

Second order phase transition for even N in the Ising universality class.

Complete center symmetry breaking for odd N.

No new constraints from free energy inequalities on these theories.

Abstract

We investigate the confining phase transition as function of temperature for theories with dynamical fermions in the two index symmetric and antisymmetric representation of the gauge group. By studying the properties of the center of the gauge group we predict for an even number of colors a confining phase transition, if second order, to be in the universality class of Ising in three dimensions. This is due to the fact that the center group symmetry does not break completely for an even number of colors. For an odd number of colors the center group symmetry breaks completely. This pattern remains unaltered at large number of colors. We claim that the confining/deconfining phase transition in these theories at large N is not mapped in the one of super Yang-Mills. We extend the Polyakov loop effective theory to describe the confining phase transition of the theories studied here for a generic number of colors. Our results are not modified when adding matter in the same higher dimensional representation of the gauge group. We comment on the interplay between confinement and chiral symmetry in these theories and suggest that they are ideal laboratories to shed light on this issue also for ordinary QCD. We compare the free energy as function of temperature for different theories. We find that the conjectured thermal inequality between the infrared and ultraviolet degrees of freedom computed using the free energy does not lead to new constraints on asymptotically free theories with fermions in higher dimensional representation of the gauge group.