| Title:
|
A gravitational effective action on a finite triangulation as a discrete model of continuous concepts (English) |
| Author:
|
Ko, Albert |
| Author:
|
Roček, Martin |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
42 |
| Issue:
|
5 |
| Year:
|
2006 |
| Pages:
|
245-251 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| MSC:
|
83C27 |
| MSC:
|
83C80 |
| idZBL:
|
Zbl 1164.83300 |
| idMR:
|
MR2322411 |
| . |
| Date available:
|
2008-06-06T22:49:37Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108031 |
| . |
| Reference:
|
[1] T. Regge: General Relativity Without Coordinates.Nuovo Cim. 19, 558 (1961). MR 0127372 |
| Reference:
|
[2] A. M. Polyakov: Quantum Geometry Of Bosonic Strings.Phys. Lett. B 103, 207 (1981). MR 0623209 |
| Reference:
|
[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). |
| Reference:
|
[4] S. Wilson: Geometric Structures on the Cochains of a Manifold.(2005). [math.GT/0505227] |
| Reference:
|
[5] A. Ko, M. Roček: A gravitational effective action on a finite triangulation.JHEP 0603, 021 (2006) [arXiv:hep-th/0512293]. MR 2221635 |
| Reference:
|
[6] Luboš Motl: .private communication. |
| . |
