Functional integration on two dimensional Regge geometries

Abstract

By adopting the standard definition of diffeomorphisms for a Regge surface we give an exact expression of the Liouville action both for the sphere and the torus topology in the discretized case. The results are obtained in a general way by choosing the unique self--adjoint extension of the Lichnerowicz operator satisfying the Riemann--Roch relation. We also give the explicit form of the integration measure for the conformal factor. For the sphere topology the theory is exactly invariant under the $SL(2,C)$ transformations, while for the torus topology we have exact translational and modular invariance. In the continuum limit the results flow into the well known expressions.

36 pages, no figures, plain latex file

References in corpus (6)

• On Functional Determinants of Laplacians in Polygons and Simplices
• Faddeev-Popov determinant in 2-dimensional Regge gravity.
• Failure of the Regge approach in two dimensional quantum gravity
• Further results on Functional Determinants of Laplacians in Simplicial Complexes
• The Ising transition in 2D simplicial quantum gravity - can Regge calculus be right?
• Conformal gauge fixing and Faddeev-Popov determinant in 2-dimensional Regge gravity

Cited by in corpus (17)

• Recent Progress in Regge Calculus
• Gauge Invariance in Simplicial Gravity
• Loop Quantum Gravity a la Aharonov-Bohm
• Spikes in Quantum Regge Calculus
• The perturbative Regge-calculus regime of Loop Quantum Gravity
• Diffeomorphism invariant measure for finite dimensional geometries
• Roaming moduli space using dynamical triangulations
• Functional integration for Regge gravity
• Discrete Gravity as a Local Theory of the Poincaré Group in the First Order Formalism
• Z_2-Regge versus Standard Regge Calculus in two dimensions
• On the Faddeev-Popov determinant in Regge calculus
• Group theoretical derivation of Liouville action for Regge surfaces
• Non invariant zeta-function regularization in quantum Liouville theory
• Simplicial Quantum Gravity on a Randomly Triangulated Sphere
• Conformal modes in simplicial quantum gravity and the Weil-Petersson volume of moduli space
• Moduli space intersection duality between Regge surfaces and 2D dynamical triangulations
• Super Liouville action for Regge surfaces