The Spectrum-generating Algebra for Bosonic Strings in a Linear Dilaton Background

TL;DR

This work develops a spectrum-generating algebra for bosonic strings in a light-like linear dilaton background by extending the framed DDF (FDDF) construction to a nontrivial, exactly solvable setting. The transverse FDDF operators retain their flat-space form in a dilaton-dependent frame, while the longitudinal Brower operators acquire explicit V-dependent deformations, yet the overall algebra remains isomorphic to the flat-space case and null Brower states decouple in d = 26. The analysis yields a modified, frame-dependent yet consistent realization of the Virasoro constraints and enables a Reggeon-type DDF construction with a deformed momentum-conservation delta function that accounts for the dilaton gradient. The results provide a controlled platform to study higher-spin massive string interactions in curved backgrounds and pave the way for exploring how LD kinematics affect scattering and chaotic behavior in string theory.

Abstract

We extend the systematic construction of bosonic DDF operators to the light-like linear dilaton background to investigate how higher-spin string states behave beyond flat spacetime. Using previous results, we show that the spectrum-generating algebra is isomorphic to the flat spacetime case up to a few subtleties. This extension provides a controlled setting to explore higher-spin massive string interactions in a nontrivial yet exactly solvable string background. Most of the derivations lead to expressions very similar to those in the flat background, with the expected modifications appearing quite naturally in the spectrum and the deformed momentum-(non)conserving delta function.