Towards a loop representation for quantum canonical supergravity
Abstract
We study several aspects of the canonical quantization of supergravity in terms of the Asthekar variables. We cast the theory in terms of a connection and we introduce a loop representation. The solution space is similar to the loop representation of ordinary gravity, the main difference being the form of the Mandelstam identities. Physical states are in general given by knot invariants that are compatible with the Mandelstam identities. There is an explicit solution to all the quantum constraint equations connected with the Chern-Simons form, which coincides exactly with the Dubrovnik version of the Kauffman Polynomial. This provides for the first time the possibility of finding explicit analytic expressions for the coefficients of that knot polynomial.
Cite
@article{arxiv.hep-th/9508036,
title = {Towards a loop representation for quantum canonical supergravity},
author = {Daniel Armand-Ugon and Rodolfo Gambini and Octavio Obregon and Jorge Pullin},
journal= {arXiv preprint arXiv:hep-th/9508036},
year = {2009}
}
Comments
12 pages Revtex, figures with epsf. An important revision was made of section four. We were able to identify the exact quantum state of all the constraints of supergravity as the Dubrovnik version of the Kauffman polynomial. This provides the first known link of that polynomial to quantum field theory