2011/05/31 by Norbert Bodendorfer, N Bodendorfer, T Thiemann +3 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Causality (physics) #Gravitino #Graviton #Loop (graph theory) #Loop quantum gravity #Multiplet #Noncommutative and Quantum Gravity Theories #Phase space #Quantum Electrodynamics and Casimir Effect #Quantum gravity #Supergravity #Supersymmetry #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/0264-9381/30/4/045007
published as Class. Quantum Grav. 30 (2013) 045007 · 12 pages. v2: Journal version. Minor clarifications and corrections
openalex publication_date 2013/01/23 · arxiv created 2013/02/12 · arxiv updated 2013/02/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 11 d 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.