BMS, String Theory, and Soft Theorems

TL;DR

This work embeds BMS asymptotic symmetries into bosonic string theory on $\mathbb{M}^d\times C$, formulating generalized Ward--Takahashi identities and boundary conditions that accommodate large diffeomorphisms in arbitrary dimensions. It develops a worldsheet perspective distinguishing large, small, and forbidden diffeomorphisms, showing how target-space diffeomorphisms act as field redefinitions while preserving a consistent BRST structure, and identifies soft graviton insertions with vacuum degeneracy arising from BMS. By analyzing path-integral measures, boundary conditions, and vertex-operator variations, the paper demonstrates that Weinberg's soft graviton theorem emerges as a generalized WT identity within string theory, with a universal soft factor that is independent of $\alpha'$ at leading order. The results suggest that string theory naturally favors boundary conditions compatible with BMS enhancements and point to extensions to superstrings and higher-dimensional generalizations, highlighting a robust link between asymptotic symmetries and soft theorems in a quantum gravitational setting.

Abstract

We study the action of the BMS group in critical, bosonic string theory living on a target space of the form $\mathbb{M}^{d}\times C$. Here $M^{d}$ is $d$-dimensional (asymptotically) flat spacetime and $C$ is an arbitrary compactification. We provide a treatment of generalized Ward--Takahashi identities and derive consistent boundary conditions for any $d$ from string theory considerations. Finally, we derive BMS transformations in higher dimensional spacetimes and show that the generalized Ward--Takahashi identity of BMS produces Weinberg's soft theorem in string theory.