2D induced quantum gravity and topological phase of the Thirring model

Abstract

We investigate a class of two-dimensional induced gravity theories in which the only fundamental degrees of freedom are fermions. The connection with gravity theories is established exactly. Within this framework, we find that the Thirring model coupled to gravity can be derived from a theory in which the underlying lagrangian is zero (modulo topological invariants). Finally, we discuss a four dimensional analog of the Thirring model. It turns out be a very appealing quantum gravity theory.