A gravitational effective action on a finite triangulation as a discrete model of continuous concepts

Albert Ko and Martin Rocek

M. Rocek, C. N. Yang Institute for Theoretical Physics, SUNY, Stony Brook, NY 11794-3840, USA
Institute for Theoretical Physics, University of Amsterdam, 1018 XE Amsterdam, The Netherlands
A. Ko, Ward Melville High School


We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimensional index theorem. We describe the construction given in {\tt hep-th/0512293} of a function that can be interpreted as a gravitational effective action on a triangulation. The variation of this function under local rescalings of the edge lengths sharing a vertex is the Euler density, and we use it to illustrate how continuous concepts can have natural discrete analogs.