Simplicial quantum gravity on a randomly triangulated sphere

Authors
Citation
C. Holm et W. Janke, Simplicial quantum gravity on a randomly triangulated sphere, INT J MOD P, 14(24), 1999, pp. 3885-3903
Citations number
27
Categorie Soggetti
Physics
Journal title
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
ISSN journal
0217751X → ACNP
Volume
14
Issue
24
Year of publication
1999
Pages
3885 - 3903
Database
ISI
SICI code
0217-751X(19990930)14:24<3885:SQGOAR>2.0.ZU;2-8
Abstract
We study 2D quantum gravity on spherical topologies employing the Regge cal culus approach with the dl/l measure. Instead of the normally used fixed no nregular triangulations we study random triangulations which are generated by the standard Voronoi-Delaunay procedure. For each system size we average the results over four different realizations of the random lattices. We co mpare both types of triangulations quantitatively and investigate how the d ifference in the expectation Value of the squared curvature, R-2, for fixed and random triangulations depends on the lattice size and the surface area A. We try to measure the string susceptibility exponents through finite-si ze scaling analyses of the expectation value of an added R-2 interaction te rm, using two conceptually quite different procedures. The approach, where an ultraviolet cutoff is held fixed in the scaling limit, is found to be pl agued with inconsistencies, as has already previously been pointed out by u s. In a conceptually different approach, where the area A is held fixed, th ese problems are not present. We find the string susceptibility exponent ga mma'(str), in rough agreement with theoretical predictions for the sphere, whereas the estimate for gamma(str), appears to be too negative. However, o ur results are hampered by the presence of severe finite-size corrections t o scaling, which lead to systematic uncertainties well above our statistica l errors. We feel that the present methods of estimating the string suscept ibilities by finite-size scaling studies are not accurate enough to serve a s testing grounds to decide the success of failure of quantum Regge calculu s.