Chiral symmetry breaking/restoration in a dyonic vacuum

Abstract

We discuss the topological phenomena in the QCD-like theories with a variable number of fundamental fermions ${N}_{f}$, focusing on the temperatures at or above the critical value ${T}_{c}$ of chiral symmetry restoration. The nonzero average of the Polyakov line, or holonomy, splits instantons into (anti)self-dual dyons, and we study both the bosonic and fermionic interactions between them. The high temperature phase is a dilute gas of ``molecules'' made of $2{N}_{c}$ dyons, neutral in topological, electric, and magnetic charges. At intermediate temperatures the diluteness of the ``molecular gas'' reaches some critical level at which chiral symmetry gets restored: we comment on why it is 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 possible structure at small and large ${N}_{f}$. We finally show that certain lattice observations are in agreement with the proposed model, and suggest a number of further lattice tests.