Abstract
Firstly, we study the state space of a massless particle on a supergroup with a reparameterization invariant action. After gauge fixing the reparameterization invariance, we compute the physical state space through the BRST cohomology and show that the quadratic Casimir Hamiltonian becomes diagonalizable in cohomology. We illustrate the general mechanism in detail in the example of a supergroup target GL(1–1). The space of physical states remains an indecomposable infinite dimensional representation of the space-time supersymmetry algebra. Secondly, we show how the full string BRST cohomology in the particle limit of string theory on AdS 3 × S 3 renders the quadratic Casimir diagonalizable, and reduces the Hilbert space to finite dimensional representations of the space-time supersymmetry algebra. Our analysis provides an efficient way to calculate the Kaluza-Klein spectrum for supergravity on AdS 3 × S 3. It may also lead to the identification of an interesting and simpler subsector of logarithmic supergroup conformal field theories, relevant to string theory.
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1Unité Mixte du CNRS et de l’Ecole Normale Supérieure associée à l’université Pierre et Marie Curie 6, UMR 8549.
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Troost, J. Massless particles on supergroups and AdS 3 × S 3 supergravity. J. High Energ. Phys. 2011, 42 (2011). https://doi.org/10.1007/JHEP07(2011)042
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DOI: https://doi.org/10.1007/JHEP07(2011)042