# BMS bootstrap BMS bootstrap is like [[0036 Conformal bootstrap|conformal bootstrap]] but with the symmetry group being the [[0064 BMS group|BMS group]]. One can do this with other symmetry groups too, but the motivations differ from case to case. The motivation for using BMS as the symmetry group is to study a potential quantum field theory living on the null infinity of asymptotically flat spacetime. ## Refs - [[2016#Bagchi, Gary, Zodinmawia]] - [[BagchiGaryZodinmawia2017]] ## Main ideas 1. Conformal symmetry -> replaced by BMS symmetry. 2. Getting states given BMS algebra -> get v.f. that generate them ($L_n$ and $M_n$) -> use these to define highest-weight states -> use raising/lowering operators (acts on these primary states) to get the rest. 3. 2&3 pt functions: Completely fixed by the global subgroup (Poincare subgroup) 4. OPE completely fixed by symmetry (except for structure constants and the spectrum of primary fields), just like CFT. 5. Further constraint: associativity of operator algebra => bootstrap equation (a constraint equation) ## Other ingredients - [[0098 BMS blocks]] - main ingredients for the solution of bootstrap equation. - BMS anomaly - [[BagchiDuttaKolekarSharma2021]][](https://arxiv.org/abs/2104.10405) - BMS modular covariance - [[BagchiMondalPalRiegler2023]][](https://arxiv.org/abs/2307.00043) ## Theories with BMS symmetry: 1. Putative FT on boundary of bulk gravity (main interest); 2. Non-relativistic conformal systems; 3. On worldsheet of tensionless string theory.