A Gravitational Effective Action on a Finite Triangulation as a Discrete Model of Continuous Concepts

Details A Gravitational Effective Action on a Finite Triangulation as a Discrete Model of Continuous Concepts A Gravitational Effective Action on a Finite Triangulation as a Discrete Model of Continuous Concepts

2006-05-02

arxiv.org/abs/hep-th/0605022v2

Physics

High Energy Physics

High Energy Physics - Theory

7 pages, 1 figure; Presented at the 26th Winter School GEOMETRY AND PHYSICS at Srni

Scientific paper

We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimen- sional index theorem. We describe the construction given in 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.

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