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

Albert Ko; Martin Roček

Archivum Mathematicum (2006)

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

Abstract

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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.

How to cite

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Ko, 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

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  1. T. Regge, General Relativity Without Coordinates, Nuovo Cim. 19, 558 (1961). (1961) MR0127372
  2. A. M. Polyakov, Quantum Geometry Of Bosonic Strings, Phys. Lett. B 103, 207 (1981). (1981) MR0623209
  3. 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) 
  4. S. Wilson, Geometric Structures on the Cochains of a Manifold, (2005). [math.GT/0505227] 
  5. A. Ko, M. Roček, A gravitational effective action on a finite triangulation, JHEP 0603, 021 (2006) [arXiv:hep-th/0512293]. MR2221635
  6. Luboš Motl, [unknown], private communication. 

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