Zero-dimensional analogue of the global gauge anomaly

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

Rotational Symmetry and A Light Mode in Two-Dimensional Staggered Fermions

To obtain a light mode in two-dimensional staggered fermions, we introduce four new local operators keeping the rotational invariance for a staggered Dirac operator. To split masses of tastes, three cases are considered. The mass matrix and the propagator for free theories are analyzed. We find that one of three cases is a good candidate for taking a single mode by the mass splitting. In the case, it is possible that a heavy mode obtains infinite mass on even sites or odd sites.Comment: 17 pages, one reference adde