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

TL;DR

This paper extends the spectrum-generating algebra for bosonic strings to a linear dilaton background, revealing similarities to flat spacetime and enabling the study of higher-spin string states in a nontrivial, exactly solvable setting.

Contribution

It systematically constructs bosonic DDF operators in a linear dilaton background, showing the algebra's isomorphism to flat spacetime and facilitating analysis of higher-spin states.

Findings

Spectrum-generating algebra remains isomorphic to flat spacetime

Expressions are similar to flat background with natural modifications

Provides a solvable setting for higher-spin string interactions

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.