Light Adjoint Quarks in the Instanton-Dyon Liquid Model IV

TL;DR

This paper extends the instanton-dyon liquid model to include adjoint quarks, analyzing how center and chiral symmetries behave at finite temperature, revealing phase transitions and symmetry breaking patterns.

Contribution

It introduces a detailed model of instanton-dyon interactions with adjoint quarks, deriving the effective theory and analyzing symmetry breaking and phase transitions.

Findings

Chiral symmetry breaks spontaneously for N_f=1.

Center symmetry is preserved in dense liquids and restored at high temperature.

Transition temperatures are estimated both numerically and analytically.

Abstract

We discuss the instanton-dyon liquid model with $N_f$ Majorana quark flavors in the adjoint representation of color $SU_c(2)$ at finite temperature. We briefly recall the index theorem on $S^1\times R^3$ for twisted adjoint fermions in a BPS dyon background of arbitrary holonomy, and use the ADHM construction to explicit the adjoint anti-periodic zero modes. We use these results to derive the partition function of an interacting instanton-dyon ensemble with $N_f$ light and anti-periodic adjoint quarks. We develop the model in details by mapping the theory on a 3-dimensional quantum effective theory with adjoint quarks with manifest $SU(N_f)\times Z_{4N_f}$ symmetry. Using a mean-field analysis at weak coupling and strong screening, we show that center symmetry requires the spontaneous breaking of chiral symmetry, which is shown to only take place for $N_f=1$. For a sufficiently dense liquid, we find that the ground state is center symmetric and breaks spontaneously flavor symmetry through $SU(N_f)\times Z_{4N_f}\rightarrow O(N_f)$. As the liquid dilutes with increasing temperature, center symmetry and chiral symmetry are restored. We present numerical and analytical estimates for the transition temperatures.