Multi-plaquette solutions for discretized Ashtekar gravity

A discretized version of canonical quantum gravity proposed by Loll is investigated. After slightly modifying Loll's discretized Hamiltonian constraint, we encode its action on the spin network states in terms of combinatorial topological manipulations of the lattice loops. Using this topological formulation we find new solutions to the discretized Wheeler-Dewitt equation. These solutions have their support on the connected set of plaquettes. We also show that these solutions are not normalizable with respect to the induced heat-kernel measure on $SL(2,{\bf C})$ gauge theories.Comment: 11 pages Latex (2 figures available as a postscript file, the rough discussion on the non-normalizability has been made exact.

Wilson Loops in Open String Theory

Wilson loop elements on torus are introduced into the partition function of open strings as Polyakov's path integral at one-loop level. Mass spectra from compactification and expected symmetry breaking are illustrated by choosing the correct weight for the contributions from annulus and M\"obius strip. We show that Jacobi's imaginary transformation connects the mass spectra with the Wilson loops. The application to thermopartition function and cosmological implications are briefly discussed.Comment: 5 pages, no figur

Transition Amplitude in 2+1 dimensional Chern-Simons Gravity on a Torus

The discussions on the modular invariance in section 5 are refined.Comment: 21 pages, Late