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

Vit Sriprachyakul

Abstract

We discuss a Wakimoto-like free field realisation of ${\frak d}(2,1;α)_1$, 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.

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

Abstract

We discuss a Wakimoto-like free field realisation of , whose subalgebra has level , 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 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.

Paper Structure

This paper contains 10 sections, 71 equations.

Table of Contents

  1. Introduction
  2. Hybrid formulation
  3. The free field realisation and the partition function
  4. Representations and Hilbert space
  5. The physical state condition and the DDF operators
  6. Conclusion and Outlook
  7. Future directions
  8. ${\frak d}(2,1;\alpha)_1$ algebra convention
  9. Dictionary between RNS and Hybrid formalisms
  10. Theta function convention