BRST Quantization of a Particle in AdS_5

TL;DR

This paper develops a BRST quantization method for a massive particle in AdS_5 using twistor variables, revealing energy quantization and connections to supermultiplets, with implications for string quantization.

Contribution

It introduces a BRST quantization framework for particles in AdS_5 with a quadratic action, deriving energy quantization conditions and linking the mass operator to algebraic moduli.

Findings

Energy E is quantized in units of 1/(2R) with integer parameters.

Physical states include a subset of massless SU(2,2) multiplets.

The approach may facilitate quantization of strings in AdS_5.

Abstract

We perform the quantization of a massive particle propagating on AdS_5. We use the twistor formulation in which the action can be brought into a quadratic form. We construct the BRST operator which commutes with AdS_5 isometries forming SU(2,2). The condition of a consistent BRST quantization requires that the AdS energy E is quantized in units of the AdS_5 radius R, E=\frac{1}{2R}(N_a +N_b+4), with N_a, N_b being some non-negative integers. We also argue that the mass operator will be identified with the moduli of the U(1) central extension Z of the SU(2,2|4) algebra in the supersymmetric case. The spectrum of physical states with vanishing ghost number contains a particular subset of `massless' SU(2,2) multiplets (including the bosonic part of the `novel short' supermultiplets). We hope that our results will help to quantize also the string on AdS_5.