A no-ghost theorem for the bosonic Nappi-Witten string

TL;DR

This paper proves a no-ghost theorem for bosonic strings in Nappi-Witten spacetime, establishing unitarity and the physical state spectrum, including spectral flow modules, thus ensuring a consistent quantum theory.

Contribution

It provides the first proof of a no-ghost theorem for bosonic strings in Nappi-Witten spacetime, extending unitarity results to this non-trivial background.

Findings

Unitarity established for NW/U(1) modules with primary states.

Physical states are contained within NW/U(1) modules.

Spectral flow modules are necessary for the full spectrum.

Abstract

We prove a no-ghost theorem for a bosonic string propagating in Nappi-Witten spacetime. This is achieved in two steps. We first demonstrate unitarity for a class of NW/U(1) modules: the norm of any state which is primary with respect to a chosen timelike U(1) is non-negative. We then show that physical states - states satisfying the Virasoro constraints - in a class of modules of an affinisation of the Nappi-Witten algebra are contained in the NW/U(1) modules. Similar to the case of strings on $AdS_3$, in order to saturate the spectrum obtained in light-cone quantization we are led to include modules with energy not bounded from below, which are related to modules with energy bounded from below by spectral flow automorphisms.