The BMS Bootstrap

TL;DR

This paper develops a bootstrap approach for two-dimensional field theories with BMS symmetry, deriving crossing equations and analytic blocks, marking a significant step beyond relativistic conformal theories.

Contribution

It introduces the BMS bootstrap framework for non-relativistic symmetries, deriving crossing symmetry and analytic BMS blocks in 2D theories with BMS3 symmetry.

Findings

Derived analytic BMS blocks at large central charge

Formulated the first bootstrap equation for BMS-invariant theories

Established a foundation for non-relativistic bootstrap studies

Abstract

We initiate a study of the bootstrap programme for field theories with BMS symmetry. Specifically, we look at two-dimensional field theories with BMS3 symmetry and, using highest weight representations, we construct the BMS bootstrap equation by formulating the notion of crossing symmetry in the four-point functions of these field theories. In the limit of large central charges, we find analytic expressions for the BMS blocks that are the basic ingredients for the solution of the bootstrap equation. This constitutes, to the best of our knowledge, the first example of the formulation and significant steps towards the solution of a bootstrap equation in a theory which is not a relativistic conformal field theory.