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

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

1995-10-07

arxiv.org/abs/hep-th/9510040v1

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

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$(L^{\dag}L)$ and ker$(LL^{\dag})$ is satisfied.

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