Superstrings on PP-Wave Backgrounds and Symmetric Orbifolds

TL;DR

This paper investigates superstring theory on a pp-wave background derived from AdS_3 x S^3 x M^4, constructing the supersymmetry algebra, analyzing the spectrum, and establishing a correspondence with symmetric orbifold conformal theory.

Contribution

It explicitly constructs the supersymmetry algebra and DDF operators for superstrings on pp-wave backgrounds and demonstrates the embedding of short string states into symmetric orbifold theory.

Findings

Spectrum classified into short and long string sectors.

Short string states correspond to BPS states in the dual theory.

Successful embedding of short string states into symmetric orbifold Hilbert space.

Abstract

We study the superstring theory on pp-wave background with NSNS-flux that is realized as the Penrose limit of AdS_3 x S^3 x M^4, where M^4 is T^4 or T^4/Z_2(~ K3). Quantizing this system in the covariant gauge, we explicitly construct the space-time supersymmetry algebra and the complete set of DDF operators. We analyse the spectrum of physical states by using the spectrally flowed representations of current algebra. This spectrum is classified by the ``short string sectors'' and the ``long string sectors'' as in AdS_3 string theory. The states of the latter propagate freely along the transverse plane of pp-wave background, but the states of the former do not. We compare the short string spectrum with the BPS and almost BPS states which have large R-charges in the symmetric orbifold conformal theory, which is known as the candidate of dual theory of superstrings on AdS_3 x S^3 x M^4. We show that every short string states can be embedded successfully in the single particle Hilbert space of symmetric orbifold conformal theory.