• DOI:10.1088/0264-9381/30/4/045007
• Corpus ID: 56562416

Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector

@article{Bodendorfer2013TowardsLQ,
  title={Towards Loop Quantum Supergravity (LQSG) II. p-Form Sector},
  author={Norbert Bodendorfer and Thomas Thiemann and Andreas Thurn},
  journal={Classical and Quantum Gravity},
  year={2013},
  volume={30},
  pages={045007}
}

• N. Bodendorfer, T. Thiemann, A. Thurn
• Published 18 May 2011
• Physics
• Classical and Quantum Gravity

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 Gaus 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.