Exact Flow Equations and the U(1)-Problem

TL;DR

This paper derives exact flow equations for SU(N) gauge theories with fermions, incorporating topologically non-trivial configurations, and analyzes the resulting U(1)-symmetry breaking effects at large infrared scales.

Contribution

It provides a novel calculation of U(1)-violating terms in the effective action using exact flow equations with infrared regularization and instanton configurations.

Findings

Explicit infrared regularization removes gauge zero modes.

Zero modes in the Dirac operator induce U_A(1) violation.

U(1)-violating terms are computed at large scales k.

Abstract

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.