Ghost-Free Spectrum of a Quantum String in SL(2,R) Curved Spacetime

TL;DR

This paper solves the unitarity problem for a quantum string in SL(2,R) curved spacetime, providing an exact, ghost-free spectrum and a new free boson realization that makes the model fully solvable.

Contribution

It introduces a ghost-free spectrum for the SL(2,R) WZW model and a novel free boson realization that ensures unitarity and solvability in curved spacetime.

Findings

Spectrum computed exactly and shown to be ghost-free

SL(2,R) currents satisfy local operator products despite logarithmic cuts

Physical states are consistent with monodromy conditions

Abstract

The unitarity problem in curved spacetime is solved for the string described by the SL(2,R) WZW model. The spectrum is computed exactly and demonstratedto be ghost-free. The new features include (i) SL(2,R) left/right symmetrycurrents that have logarithmic cuts on the world sheet but that satisfy theusual local operator products or commutation rules, (ii) physical statesconsistent with the monodromy condition of closed strings despite thelogarithmic singularity in the currents, and (iii) a new free boson realization for these currents which render the SL(2,R) WZW model completely solvable.