Massless particles on supergroups and AdS3 x S3 supergravity

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 AdS3 x S3 renders the quadratic Casimir diagonalizable, and reduces the Hilbert space to finite dimensional representations of the space-time supersymmetry algebra (after analytic continuation). Our analysis provides an efficient way to calculate the Kaluza-Klein spectrum for supergravity on AdS3 x S3. It may also be a step towards the identification of an interesting and simpler subsector of logarithmic supergroup conformal field theories, relevant to string theory.

16 pages, 10 figures

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• Superstrings in AdS
• Superspace conformal field theory
• String States on AdS_3 x S^3 from the Supergroup
• The massless string spectrum on AdS_3 x S^3 from the supergroup
• The free field realisation of the BVW string
• Finite dimensional vertex
• The plane-wave limit of ${\mathrm{AdS}}_3\times {\mathrm{S}}^3\times {\mathrm{S}}^3\times {\mathrm{S}}^1$
• Models for Modules
• The physical states of the Hybrid Formalism
• On the gl(1|1) Wess-Zumino-Witten Model
• String theory in twistor space and minimal tension holography