The Chiral Symmetry Breaking/Restoration in Dyonic Vacuum

TL;DR

This paper investigates topological phenomena in QCD-like theories at high temperatures, focusing on dyonic configurations and their role in chiral symmetry restoration, with implications for lattice observations.

Contribution

It introduces a detailed analysis of dyon interactions and their impact on chiral symmetry restoration in theories with fundamental and adjoint fermions, providing new insights into the high-temperature phase structure.

Findings

High temperature phase is a dilute gas of neutral dyon molecules.

Chiral symmetry restoration occurs at a critical diluteness level.

The ensemble transitions to a strongly coupled liquid with short-range order.

Abstract

We discuss the topological phenomena in the QCD-like theories with variable number of fundamental $N_f$ or adjoint $N_a$ fermions, focusing on the temperatures at or above the critical value $T_c$ of chiral symmetry restoration. Nonzero average of the Polyakov line, or holonomy, splits instantons into (anti)selfdual dyons, and we study both bosonic and fermionic interactions between them. The high temperature phase is a dilute gas of "molecules" made of $2N_c$ dyons, neutral in topological, electric and magnetic charges. At intermediate temperatures the diluteness reaches some critical level at which chiral symmetry gets restored: we explain why it is very different for the fundamental and adjoint fermions. At high density the ensemble is a strongly coupled liquid with crystal-like short range order: we speculate about its structure at small and large $N_f$. We finally explaine certain lattice observations and suggest a number of further lattice tests.