A Comment on Continuous Spin Representations of the Poincaré Group and Perturbative String Theory

TL;DR

The paper argues that massless continuous spin representations (CSRs) of the Poincaré group are not realized in perturbative string theory, making their absence a model-independent low-energy prediction. By analyzing the Poincaré algebra and the light-cone string spectrum, it shows that the CSR-generating translations $\Pi^i$ annihilate massless string states, eliminating the infinite-multiplet structure of CSR. The result reinforces that standard string constructions realize only helicity-like massless states and aligns with the non-observation of CSRs in nature, with caveats about non-perturbative or extreme limits. Overall, CSRs provide a sharp constraint on string theory realizations and distinguish standard perturbative spectra from hypothetical CSR sectors.

Abstract

We make a simple observation that the massless continuous spin representations of the Poincaré group are not present in perturbative string theory constructions. This represents one of the very few model-independent low-energy consequences of these models.