The physical states of the Hybrid Formalism

TL;DR

This paper analyzes the physical states of string theory on AdS3×S3×T4 with minimal flux using the hybrid formalism, explicitly identifying low-lying states and confirming their dual CFT correspondence through correlator calculations.

Contribution

It explicitly constructs BRST cohomology classes for low-lying states in the hybrid formalism at k=1 and confirms their dual CFT counterparts via correlator computations.

Findings

Explicit identification of BRST cohomology classes for low-lying states.

Matching of worldsheet correlators with dual CFT predictions.

Simplification of vertex operators using an alternative BRST choice.

Abstract

String theory on ${\rm AdS}_3\times {\rm S}^3 \times\mathbb{T}^4$ with one unit ($k=1$) of NS-NS flux is considered in the hybrid formalism of Berkovits, Vafa & Witten (BVW). Using the free field realisation of the world-sheet theory at $k=1$, we identify explicitly the BRST cohomology classes corresponding to some of the low-lying states of the dual CFT. In particular, we do this for the ${\cal N}=4$ superconformal generators of the symmetric orbifold theory, and we confirm these identifications by showing that the worldsheet correlators reproduce the expected dual CFT answer. Along the way we note that the physical vertex operators on the worldsheet have a simpler form if one works with a different, but equivalent, choice for the BRST operators relative to BVW.