On the Faddeev-Popov determinant in Regge calculus

The functional integral measure in the 4D Regge calculus normalised w.r.t. the DeWitt supermetric on the space of metrics is considered. The Faddeev-Popov factor in the measure is shown according to the previous author's work on the continuous fields in Regge calculus to be generally ill-defined due to the conical singularities. Possible resolution of this problem is discretisation of the gravity ghost (gauge) field by, e.g., confining ourselves to the affine transformations of the affine frames in the simplices. This results in the singularity of the functional measure in the vicinity of the flat background, where part of the physical degrees of freedom connected with linklengths become gauge ones.Comment: 5 pages, LaTe

Super Liouville action for Regge surfaces

We compute the super Liouville action for a two dimensional Regge surface by exploiting the invariance of the theory under the superconformal group for sphere topology and under the supermodular group for torus topology. For sphere topology and torus topology with even spin structures, the action is completely fixed up to a term which in the continuum limit goes over to a topological invariant, while the overall normalization of the action can be taken from perturbation theory. For the odd spin structure on the torus, due to the presence of the fermionic supermodulus, the action is fixed up to a modular invariant quadratic polynomial in the fermionic zero modes.Comment: 18 pages, LaTe

Group theoretical derivation of Liouville action for Regge surfaces

We show that the structure of the Liouville action on a two dimensional Regge surface of the topology of the sphere and of the torus is determined by the invariance under the transformations induced by the conformal Killing vector fields and under modular transformations.Comment: 10 pages, LaTex fil