The BMS Bootstrap

TL;DR

This work develops a bootstrap framework for 2d field theories with BMS3 symmetry, extending bootstrap techniques beyond relativistic CFTs. It constructs the plane representation, primary states labeled by $(\Delta,\xi)$, and a BMS operator product expansion whose descendant data are fixed by symmetry, then formulates a crossing equation for four-point functions in terms of BMS blocks. In the large central charge limit, the authors derive closed-form global BMS blocks and show they satisfy Casimir-based differential equations, providing a concrete handle on solving the BMS bootstrap. The results advance flat-space holography and the study of Galilean conformal field theories by offering a principled method to constrain BMS-invariant theories and their possible holographic duals, with future directions including holographic realizations via flat-space geodesic Witten diagrams and exploration of minimal GCFT models.

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.