Bodendorfer N, Thiemann T, Thurn A (2013)
Publication Status: Published
Publication Type: Journal article
Publication year: 2013
Publisher: IOP PUBLISHING LTD
Book Volume: 30
Journal Issue: 4
DOI: 10.1088/0264-9381/30/4/045007
In our companion paper, we focused on the quantization of the Rarita-Schwinger 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 3-index photon of minimal 11d SUGRA, but our methods easily extend to more general p-form fields. Due to the presence of a Chern-Simons term for the 3-index photon, which is due to local SUSY, the theory is self-interacting and its quantization far from straightforward. Nevertheless, we show that a reduced phase space quantization with respect to the 3-index 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 Chern-Simons theory, admits a background independent state of the Narnhofer-Thirring type.
APA:
Bodendorfer, N., Thiemann, T., & Thurn, A. (2013). Towards loop quantum supergravity (LQSG): II. p-form sector. Classical and Quantum Gravity, 30(4). https://dx.doi.org/10.1088/0264-9381/30/4/045007
MLA:
Bodendorfer, Norbert, Thomas Thiemann, and Andreas Thurn. "Towards loop quantum supergravity (LQSG): II. p-form sector." Classical and Quantum Gravity 30.4 (2013).
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