Towards loop quantum supergravity (LQSG): I. Rarita-Schwinger sector

Journal article


Publication Details

Author(s): Bodendorfer N, Thiemann T, Thurn A
Journal: Classical and Quantum Gravity
Publisher: IOP PUBLISHING LTD
Publication year: 2013
Volume: 30
Journal issue: 4
ISSN: 0264-9381


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 Poisson-commuting, 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 11D SUGRA and 4D, 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 Rarita-Schwinger field. This is non-trivial because SUSY typically requires the Rarita-Schwinger 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 background-independent representation of the non-trivial Dirac antibracket *-algebra for the Majorana field which significantly differs from the analogous construction for Dirac fields already available in the literature.



FAU Authors / FAU Editors

Bodendorfer, Norbert
Lehrstuhl für Theoretische Physik
Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik
Thurn, Andreas
Lehrstuhl für Theoretische Physik


How to cite

APA:
Bodendorfer, N., Thiemann, T., & Thurn, A. (2013). Towards loop quantum supergravity (LQSG): I. Rarita-Schwinger sector. Classical and Quantum Gravity, 30(4). https://dx.doi.org/10.1088/0264-9381/30/4/045006

MLA:
Bodendorfer, Norbert, Thomas Thiemann, and Andreas Thurn. "Towards loop quantum supergravity (LQSG): I. Rarita-Schwinger sector." Classical and Quantum Gravity 30.4 (2013).

BibTeX: 

Last updated on 2018-19-04 at 04:11