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arXiv · 0907.5366

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

Gang Chen·Yeuk-Kwan E. Cheung·Zheyong Fan·Jens Fjelstad·Stephen Hwang
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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.

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Gang Chen, Yeuk-Kwan E. Cheung, Zheyong Fan, Jens Fjelstad, Stephen Hwang. 2009-07-30. A no-ghost theorem for the bosonic Nappi-Witten string. https://doi.org/10.1103/physrevd.80.086003

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