Massless particles on supergroups and AdS3 x S3 supergravity

TL;DR

This paper investigates the state space of massless particles on supergroups and their implications for supergravity on AdS3 x S3, revealing how BRST cohomology simplifies the spectrum and aids in spectrum calculations.

Contribution

It introduces a method to analyze the physical state space using BRST cohomology, demonstrating diagonalizability of the quadratic Casimir and simplifying supergravity spectrum computations.

Findings

Quadratic Casimir becomes diagonalizable in cohomology.

Physical states form indecomposable infinite dimensional representations.

Method reduces Hilbert space to finite dimensional representations.

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.