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

Archivum Mathematicum (2006)

- Volume: 042, Issue: 5, page 245-251
- ISSN: 0044-8753

## Access Full Article

top## Abstract

top## How to cite

topKo, Albert, and Roček, Martin. "A gravitational effective action on a finite triangulation as a discrete model of continuous concepts." Archivum Mathematicum 042.5 (2006): 245-251. <http://eudml.org/doc/249812>.

@article{Ko2006,

abstract = {We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimensional 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.},

author = {Ko, Albert, Roček, Martin},

journal = {Archivum Mathematicum},

keywords = {Gauss-Bonnet theorem; gravitational effective action; rescaling},

language = {eng},

number = {5},

pages = {245-251},

publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},

title = {A gravitational effective action on a finite triangulation as a discrete model of continuous concepts},

url = {http://eudml.org/doc/249812},

volume = {042},

year = {2006},

}

TY - JOUR

AU - Ko, Albert

AU - Roček, Martin

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

JO - Archivum Mathematicum

PY - 2006

PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno

VL - 042

IS - 5

SP - 245

EP - 251

AB - We recall how the Gauss-Bonnet theorem can be interpreted as a finite dimensional 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.

LA - eng

KW - Gauss-Bonnet theorem; gravitational effective action; rescaling

UR - http://eudml.org/doc/249812

ER -

## References

top- T. Regge, General Relativity Without Coordinates, Nuovo Cim. 19, 558 (1961). (1961) MR0127372
- A. M. Polyakov, Quantum Geometry Of Bosonic Strings, Phys. Lett. B 103, 207 (1981). (1981) MR0623209
- D. M. Capper, M. J. Duff, Trace Anomalies In Dimensional Regularization, Nuovo Cim. A 23, 173 (1974); M. J. Duff, Observations On Conformal Anomalies, Nucl. Phys. B 125, 334 (1977). (1974)
- S. Wilson, Geometric Structures on the Cochains of a Manifold, (2005). [math.GT/0505227]
- A. Ko, M. Roček, A gravitational effective action on a finite triangulation, JHEP 0603, 021 (2006) [arXiv:hep-th/0512293]. MR2221635
- Luboš Motl, [unknown], private communication.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.