Zero-dimensional analogue of the global gauge anomaly

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.

arXiv comment6 pages, uses PTPTeX.cls, the final version to appear in Prog. Theor. Phys