Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum

TL;DR

This paper analyzes the spectrum of bosonic strings in AdS_3 using the SL(2,R) WZW model, identifying symmetries, classifying states, and establishing a no-ghost theorem for the involved representations.

Contribution

It provides a detailed spectral analysis of bosonic strings in AdS_3, including classical solutions, symmetries, and a proof of the no-ghost theorem for relevant representations.

Findings

Identification of a symmetry relating string configurations with different winding numbers

A comprehensive description of the Hilbert space including long strings

Proof of the no-ghost theorem for the involved representations

Abstract

In this paper we study the spectrum of bosonic string theory on AdS_3. We study classical solutions of the SL(2,R) WZW model, including solutions for long strings with non-zero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a no-ghost theorem for all the representations that are involved and discuss the scattering of the long string.