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 $\text{SO}(2N)$ 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 $\text{SU}(2N_c)$ 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.

Comments: 6 pages, uses PTPTeX.cls, the final version to appear in Prog. Theor. Phys