# 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.