Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Summary:
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.
References:
[1] T. Regge: General Relativity Without Coordinates. Nuovo Cim. 19, 558 (1961). MR 0127372
[2] A. M. Polyakov: Quantum Geometry Of Bosonic Strings. Phys. Lett. B 103, 207 (1981). MR 0623209
[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).
[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]. MR 2221635
[6] Luboš Motl: private communication.
Search
Partner of
