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

Albert Ko·Martin Rocek
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Abstract

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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Albert Ko, Martin Rocek. 2006-05-04. A Gravitational Effective Action on a Finite Triangulation as a Discrete Model of Continuous Concepts. https://arxiv.org/abs/hep-th/0605022

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