Conformal gauge fixing and Faddeev-Popov determinant in 2-dimensional Regge gravity

Abstract

By regularizing the conical singularities by means of a segment of a sphere or pseudosphere and then taking the regulator to zero, we compute exactly the Faddeev--Popov determinant related to the conformal gauge fixing for a piece-wise flat surface with the topology of the sphere. The result is analytic in the opening angles of the conical singularities in the interval ($\pi$, $4\pi$) and in the smooth limit goes over to the continuum expression. The Riemann-Roch relation on the dimensions of ker$(L^{†}L)$ and ker$(L{L}^{†})$ is satisfied.

Comments: 8 pages, latex. Talk given at the XVIII International Workshop on High Energy Physics and Field Theory; Protvino, Russia, June 1995