String Theory in the Penrose Limit of AdS_2 x S^2

TL;DR

This paper explores string theory in a specific plane-wave background derived from AdS_2 x S^2, revealing new representations of the underlying algebra, constructing the spectrum with free fields, and confirming unitarity and correct vertex operator properties.

Contribution

It introduces previously missed continuous series representations of the algebra, constructs the string spectrum using free fields, and demonstrates unitarity without additional constraints.

Findings

New continuous series representations of h_4 algebra identified

Spectrum constructed with free bosonic fields and shown to be ghost-free

Vertex operators have correct conformal properties and unitarity confirmed

Abstract

The string theory in the Penrose limit of AdS_2 x S^2 is investigated. The specific Penrose limit is the background known as the Nappi-Witten spacetime, which is a plane-wave background with an axion field. The string theory on it is given as the Wess-Zumino-Novikov-Witten (WZNW) model on non-semi-simple group H_4. It is found that, in the past literature, an important type of irreducible representations of the corresponding algebra, h_4, were missed. We present this "new" representations, which have the type of continuous series representations. All the three types of representations of the previous literature can be obtained from the "new" representations by setting the momenta in the theory to special values. Then we realized the affine currents of the WZNW model in terms of four bosonic free fields and constructed the spectrum of the theory by acting the negative frequency modes of free fields on the ground level states in the h_4 continuous series representation. The spectrum is shown to be free of ghosts, after the Virasoro constraints are satisfied. In particular we argued that there is no need for constraining one of the longitudinal momenta to have unitarity. The tachyon vertex operator, that correspond to a particular state in the ground level of the string spectrum, is constructed. The operator products of the vertex operator with the currents and the energy-momentum tensor are shown to have the correct forms, with the correct conformal weight of the vertex operator.