The nuts and bolts of the BMS Bootstrap

TL;DR

The paper extends the conformal bootstrap framework to 2d theories with BMS3 symmetry by formulating a BMS OPE, constructing BMS blocks, and deriving a BMS crossing equation. It develops an intrinsic analysis based on highest-weight representations and, separately, a limiting analysis via two 2d Virasoro contractions to reproduce the BMS results, including explicit global blocks and OPE coefficients up to level 2. The work demonstrates consistency with non-relativistic contractions from 2d CFTs and explores a chiral limit where BMS3 reduces to a Virasoro algebra, with holographic checks in flatspace gravity. These results provide a structured path toward classifying 2d BMS-invariant theories and their holographic duals in flat spacetimes. The paper thus establishes foundational tools for flat-space holography, non-relativistic conformal systems, and potential supersymmetric extensions of the BMS bootstrap.

Abstract

In this paper, we elaborate on aspects of the recently introduced BMS bootstrap programme. We consider two-dimensional (2d) field theories with BMS3 symmetry and extensively use highest weight representations to uncover the BMS version of crossing symmetry in 4-point functions that are constrained by symmetry. The BMS bootstrap equation is formulated and then analytic expressions for BMS blocks are constructed by looking at the limit of large central charges. These results are also applicable to 2d Galilean Conformal Field Theories through the isomorphism between the BMS3 and 2d Galilean Conformal Algebras. We recover our previously obtained results in the non-relativistic limit of the corresponding ones in 2d relativistic CFTs. This provides a comprehensive check of our previous analysis. We also explore the chiral limit of BMS3 where the BMS algebra reduces to a single copy of the Virasoro algebra and show that our analysis is consistent with earlier work in this direction.