Conformal modes in simplicial quantum gravity and the Weil-Petersson
volume of moduli space
M. Carfora, and A. Marzuoli. (2001)cite arxiv:math-ph/0107028
Comment: 48 pages Latex; corrected typos; added an appendix on the connection
with curvature assignments entropy estimates.
Abstract
Our goal here is to present a detailed analysis connecting the anomalous
scaling properties of 2D simplicial quantum gravity to the geometry of the
moduli space M_g,N of genus g Riemann surfaces with N punctures. In the case
of pure gravity we prove that the scaling properties of the set of dynamical
triangulations with N vertices are directly provided by the large N asymptotics
of the Weil-Petersson volume of M_g,N, recently discussed by Manin and
Zograf. Such a geometrical characterization explains why dynamical
triangulations automatically take into account the anomalous scaling properties
of Liouville theory. In the case of coupling with conformal matter we briefly
argue that the anomalous scaling of the resulting discretized theory should be
related to the Gromov-Witten invariants of the moduli space M_g,N(X,\beta) of
stable maps from (punctured Riemann surfaces associated with) dynamical
triangulations to a manifold X parameterizing the conformal matter
configurations.
Description
[math-ph/0107028] Conformal modes in simplicial quantum gravity and the Weil-Petersson volume of moduli space
%0 Generic
%1 Carfora2001
%A Carfora, Mauro
%A Marzuoli, Annalisa
%D 2001
%K conformal gravity moduli
%T Conformal modes in simplicial quantum gravity and the Weil-Petersson
volume of moduli space
%U http://arxiv.org/abs/math-ph/0107028
%X Our goal here is to present a detailed analysis connecting the anomalous
scaling properties of 2D simplicial quantum gravity to the geometry of the
moduli space M_g,N of genus g Riemann surfaces with N punctures. In the case
of pure gravity we prove that the scaling properties of the set of dynamical
triangulations with N vertices are directly provided by the large N asymptotics
of the Weil-Petersson volume of M_g,N, recently discussed by Manin and
Zograf. Such a geometrical characterization explains why dynamical
triangulations automatically take into account the anomalous scaling properties
of Liouville theory. In the case of coupling with conformal matter we briefly
argue that the anomalous scaling of the resulting discretized theory should be
related to the Gromov-Witten invariants of the moduli space M_g,N(X,\beta) of
stable maps from (punctured Riemann surfaces associated with) dynamical
triangulations to a manifold X parameterizing the conformal matter
configurations.
@misc{Carfora2001,
abstract = { Our goal here is to present a detailed analysis connecting the anomalous
scaling properties of 2D simplicial quantum gravity to the geometry of the
moduli space M_{g,N} of genus g Riemann surfaces with N punctures. In the case
of pure gravity we prove that the scaling properties of the set of dynamical
triangulations with N vertices are directly provided by the large N asymptotics
of the Weil-Petersson volume of M_{g,N}, recently discussed by Manin and
Zograf. Such a geometrical characterization explains why dynamical
triangulations automatically take into account the anomalous scaling properties
of Liouville theory. In the case of coupling with conformal matter we briefly
argue that the anomalous scaling of the resulting discretized theory should be
related to the Gromov-Witten invariants of the moduli space M_{g,N}(X,\beta) of
stable maps from (punctured Riemann surfaces associated with) dynamical
triangulations to a manifold X parameterizing the conformal matter
configurations.
},
added-at = {2010-01-29T17:24:42.000+0100},
author = {Carfora, Mauro and Marzuoli, Annalisa},
biburl = {https://www.bibsonomy.org/bibtex/2ff7900b5d7ddef41160f51984f57d1c8/uludag},
description = {[math-ph/0107028] Conformal modes in simplicial quantum gravity and the Weil-Petersson volume of moduli space},
interhash = {578221256301708bf021b7be95447923},
intrahash = {ff7900b5d7ddef41160f51984f57d1c8},
keywords = {conformal gravity moduli},
note = {cite arxiv:math-ph/0107028
Comment: 48 pages Latex; corrected typos; added an appendix on the connection
with curvature assignments entropy estimates},
timestamp = {2010-01-29T17:24:42.000+0100},
title = {Conformal modes in simplicial quantum gravity and the Weil-Petersson
volume of moduli space},
url = {http://arxiv.org/abs/math-ph/0107028},
year = 2001
}