Tensionless hybrid strings in $\rm AdS_3\times S^3\times S^3\times S^1$: Free field realisation

TL;DR

This paper presents a free field realization of a specific current algebra in AdS3 backgrounds, computes the string partition function, and matches it with a symmetric orbifold theory, providing insights into string spectra.

Contribution

It introduces a Wakimoto-like free field realization of ${rak d}(2,1; alpha)_1$ that exactly realizes the current algebra without gauging, and connects the string partition function to a symmetric orbifold model.

Findings

The full string partition function matches the symmetric orbifold of free fields.

The realization requires no gauging, simplifying the analysis.

The paper discusses DDF operators and physical state conditions.

Abstract

We discuss a Wakimoto-like free field realisation of ${\frak d}(2,1;\alpha)_1$, whose $\frak{sl}(2,\mathbb{R})$ subalgebra has level $k=1$, that requires no gauging, i.e., realises the current algebra exactly. We then compute the partition function of the theory and show that, by combining this with the ghost contribution, the full, on-shell projected string partition function reproduces precisely the single-particle partition function of the ${\rm Sym}^N({\cal S'}_0^2)$ theory, i.e. the symmetric orbifold theory of 8 free fermions, 1 compact free boson, and 1 non-compact free boson. We also discuss other aspects such as DDF operators and BRST and physical state conditions.