Towards loop quantum supergravity (LQSG): I. RaritaSchwinger sector
Abstract
In our companion papers, we managed to derive a connection formulation of Lorentzian general relativity in D + 1 dimensions with compact gauge group SO(D + 1) such that the connection is Poissoncommuting, which implies that loop quantum gravity quantization methods apply. We also provided the coupling to standard matter. In this paper, we extend our methods to derive a connection formulation of a large class of Lorentzian signature supergravity theories, in particular 11 D SUGRA and 4 D, N = 8 SUGRA, which was in fact the motivation to consider higher dimensions. Starting from a Hamiltonian formulation in the time gauge which yields a Spin(D) theory, a major challenge is to extend the internal gauge group to Spin(D + 1) in the presence of the RaritaSchwinger field. This is nontrivial because SUSY typically requires the RaritaSchwinger field to be a Majorana fermion for the Lorentzian Clifford algebra and Majorana representations of the Clifford algebra are not available in the same spacetime dimension for both Lorentzian and Euclidean signatures. We resolve the arising tension and provide a backgroundindependent representation of the nontrivial Dirac antibracket *algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature.
 Publication:

Classical and Quantum Gravity
 Pub Date:
 February 2013
 DOI:
 10.1088/02649381/30/4/045006
 arXiv:
 arXiv:1105.3709
 Bibcode:
 2013CQGra..30d5006B
 Keywords:

 General Relativity and Quantum Cosmology;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 43 pages. v2: Journal version. Some nonessential sign errors in sections 2 and 3 corrected. Minor clarifications and corrections