The 't Hooft vertex revisited

TL;DR

This paper revisits 't Hooft's 1976 approach to topological effects in non-Abelian gauge theories, emphasizing the role of effective multi-fermion interactions and their implications for chiral symmetries, quark masses, and lattice simulations.

Contribution

It clarifies the significance of 't Hooft's vertex in modern theoretical and computational contexts, connecting historical insights with current debates.

Findings

Reaffirmation of 't Hooft's effective interaction as fundamental.

Insights into discrete chiral symmetries and quark mass ambiguities.

Identification of potential issues in lattice gauge theory algorithms.

Abstract

In 1976 't Hooft introduced an elegant approach towards understanding the physical consequences of the topological structures that appear in non-Abelian gauge theories. These effects are concisely summarized in terms of an effective multi-fermion interaction. These old arguments provide a link between a variety of recent and sometimes controversial ideas including discrete chiral symmetries appearing in some models for unification, ambiguities in the definition of quark masses, and flaws with some simulation algorithms in lattice gauge theory.