Zero-dimensional analogue of the global gauge anomaly

TL;DR

This paper explores a zero-dimensional analogue of Witten's global gauge anomaly, revealing how certain reduced Yang-Mills theories with Majorana fermions exhibit anomalies leading to indeterminate or infinite expectation values.

Contribution

It introduces a zero-dimensional framework to analyze global gauge anomalies, providing new insights into the behavior of reduced Yang-Mills theories with Majorana fermions.

Findings

Reduction of 2D $ ext{SO}(2N)$ Yang-Mills with Majorana-Weyl fermion shows anomaly effects.

Reduction of 2D/3D $ ext{SU}(2N_c)$ Yang-Mills with adjoint Majorana fermion leads to indeterminate or infinite expectation values.

Zero-dimensional models capture essential features of global gauge anomalies in higher dimensions.

Abstract

A zero-dimensional analogue of Witten's global gauge anomaly is considered. For example, a zero-dimensional reduction of the two-dimensional $\SO(2N)$ Yang-Mills theory with a single Majorana-Weyl fermion in the fundamental representation suffers from this anomaly. Another example is a zero-dimensional reduction of two- and three-dimensional $\SU(2N_c)$ Yang-Mills theories which couple to a single Majorana fermion in the adjoint representation. In this case, any expectation value is either indeterminate or infinite.