The no-ghost theorem for string theory in curved backgrounds with a flat timelike direction

Abstract

It is well-known that the standard no-ghost theorem can be extended straightforwardly to the general c = 26 CFT on IR d−1,1 × K, where 2 ≤ d ≤ 26 and K is a compact unitary CFT of appropriate central charge. We prove the no-ghost theorem for d = 1, i.e., when only the timelike direction is flat. This is done using the technique of Frenkel, Garland and Zuckerman.

Quantum gravity from timelike Liouville theory

“…We comment on the effect of the cosmological constant in §4.3 and prove the no-ghost theorem by imposing hermiticity of the matter sector. We follow the formalism of [14] rather than the more recent and general method in [60] which requires only a single flat timelike direction. Our reasons are two fold.…”

Gauge Fixing and Scattering Amplitudes in String Field Theory Expanded around Universal Solutions

“…13)-16) The perturbative equation of motion for the fluctuation is given by Q B (a)Φ = 0. Because the modified and original BRS charges are related by the similarity transformation (2 .…”

Physical state representations and gauge fixing in string theory

“…Actually, in ref. [9,10], BRST quantization of string theory on curved background represented by the CFT of the form (c 0 = 1, h 0 < 0) ⊗ (c K = 25, h K > 0) was considered and the claim that there were no negative-norm states in the observable Hilbert space was made. The logic used there was that the states with ghosts (b −n , c −n ) or time-like states (α 0 −n ) can decouple from observable Hilbert space.…”

“…The logic used there was that the states with ghosts (b −n , c −n ) or time-like states (α 0 −n ) can decouple from observable Hilbert space. Our present work for β = 0 corresponds to giving explicit representation of the corresponding observable Hilbert space (without b −n , c −n and α 0 −n ) that had not been explicitly specified in [9,10]. Furthermore, to proceed our discussion, we would like to find out whether the possible additional gauge conditions are expressed in simpler forms in terms of BRST quantization.…”