Fermions and Gravitational Anomaly in Lattice Gravity

Kahler's geometrical description of fermions without the use of spinors is extended to the systems on general discretized manifolds. It is shown that this prescription gives a generalized version of the Susskind fermions. In this framework the interaction between fermions and lattice gravity is studied. The effective action obtained from the functional integrals in two·dimensional space · time shows the existence of the lattice analogues of the trace anomaly and the gravitational anomaly