Chiral symmetry breaking and theta vacuum structure in QCD

TL;DR

This paper revisits the mechanisms of chiral symmetry breaking and theta vacuum structure in QCD, emphasizing the role of gauge topology and gauge transformations, with insights from the Schwinger model.

Contribution

It provides a mathematically consistent analysis of axial U(1) problem and theta vacua in QCD using the temporal gauge, including strong and weak Gauss law scenarios.

Findings

Reproduction of general results by the Schwinger model in temporal gauge

Clarification of gauge topology's role in symmetry breaking

Analysis of gauge transformation localization and chiral symmetry generation

Abstract

The solution of the axial U(1) problem, the role of the topology of the gauge group in forcing the breaking of axial symmetry in any irreducible representation of the observable algebra and the theta vacua structure are revisited in the temporal gauge with attention to the mathematical consistency of the derivations. Both realizations with strong and weak Gauss law are discussed; the control of the general mechanisms and structures is obtained on the basis of the localization of the (large) gauge transformations and the local generation of the chiral symmetry. The Schwinger model in the temporal gauge exactly reproduces the general results.