Towards loop quantum supergravity (LQSG): II. pform sector
Abstract
In our companion paper, we focused on the quantization of the RaritaSchwinger sector of supergravity theories in various dimensions by using an extension of loop quantum gravity to all spacetime dimensions. In this paper, we extend this analysis by considering the quantization of additional bosonic fields necessary to obtain a complete SUSY multiplet next to graviton and gravitino in various dimensions. As a generic example, we study concretely the quantization of the 3index photon of minimal 11d SUGRA, but our methods easily extend to more general pform fields. Due to the presence of a ChernSimons term for the 3index photon, which is due to local SUSY, the theory is selfinteracting and its quantization far from straightforward. Nevertheless, we show that a reduced phase space quantization with respect to the 3index photon Gauß constraint is possible. Specifically, the Weyl algebra of observables, which deviates from the usual CCR Weyl algebras by an interesting twist contribution proportional to the level of the ChernSimons theory, admits a background independent state of the NarnhoferThirring type.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 February 2013
 DOI:
 10.1088/02649381/30/4/045007
 arXiv:
 arXiv:1105.3710
 Bibcode:
 2013CQGra..30d5007B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 12 pages. v2: Journal version. Minor clarifications and corrections