The BRST quantization and the no-ghost theorem for AdS_3

TL;DR

This paper extends the proof of the no-ghost theorem to AdS_3 backgrounds using BRST quantization, establishing equivalence with the OCQ approach and highlighting the structure of the matter Hilbert space.

Contribution

It provides the first proof of the no-ghost theorem for AdS_3 in the BRST framework and compares it with the OCQ method, demonstrating their equivalence.

Findings

Proved the no-ghost theorem for AdS_3 using BRST quantization.

Established the BRST-OCQ equivalence for AdS_3.

Identified the structure of the matter Hilbert space as a product of two Verma modules.

Abstract

In our previous papers, we prove the no-ghost theorem without light-cone directions (hep-th/0005002, hep-th/0303051). We point out that our results are valid for more general backgrounds. In particular, we prove the no-ghost theorem for AdS_3 in the context of the BRST quantization (with the standard restriction on the spin). We compare our BRST proof with the OCQ proof and establish the BRST-OCQ equivalence for AdS_3. The key in both approaches lies in the certain structure of the matter Hilbert space as a product of two Verma modules. We also present the no-ghost theorem in the most general form.