Topology, quantum gravity and particle physics

Abstract

It is argued that quantum gravity has an interpretation as a topological quantum field theory provided a certain constraint from the path integral measure is respected.The constraint forces us to couple gauge and matter fields to gravity for space -time dimensions different from 3. We then discuss possible models which may be relevant to our universe.

Topological Gravity on (D,N)-Shift Superspace Formulation

“…Thus, it is possible to formulate an immediate extension to an arbitrary superspace dimension [9]. We think it is possible to proceed seemingly for topological gravity [13], that is, to describe this theory in a topological formalism, based on supersymmetry (SUSY, from now on): a supersymmetric topological gravity [14]. We accomplished this construction by exploiting the shift supersymmetry formalism, and defining the geometric supersymmetric elements of the theory from an extension of the usual elements of the differential Riemannian formulation.…”