PIRSA:22100112

# Local supersymmetry as square roots of supertranslations: A Hamiltonian study

### APA

Majumdar, S. (2022). Local supersymmetry as square roots of supertranslations: A Hamiltonian study. Perimeter Institute. https://pirsa.org/22100112

### MLA

Majumdar, Sucheta. Local supersymmetry as square roots of supertranslations: A Hamiltonian study. Perimeter Institute, Oct. 13, 2022, https://pirsa.org/22100112

### BibTex

```          @misc{ pirsa_22100112,
doi = {10.48660/22100112},
url = {https://pirsa.org/22100112},
author = {Majumdar, Sucheta},
keywords = {Quantum Gravity},
language = {en},
title = {Local supersymmetry as square roots of supertranslations: A Hamiltonian study},
publisher = {Perimeter Institute},
year = {2022},
month = {oct},
note = {PIRSA:22100112 see, \url{https://pirsa.org}}
}
```

Sucheta Majumdar École Normale Supérieure de Lyon (ENS Lyon)

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## Abstract

In this talk, I will show that supergravity on asymptotically flat spaces possesses a (nonlinear) asymptotic symmetry algebra, containing an infinite number of fermionic generators. Starting from the Hamiltonian action for supergravity with suitable boundary conditions on the graviton and gravitino fields, I will derive a graded extension of the BMS_4 algebra at spatial infinity, denoted by SBMS_4. These boundary conditions are not only invariant under the SBMS_4 algebra, but lead to a fully consistent canonical description of the supersymmetries, which have well-defined Hamiltonian generators. One finds, in particular, that the graded brackets between the fermionic generators yield BMS supertranslations, of which they provide therefore “square roots”.  I will comment on some key aspects of extending the asymptotic analysis at spatial infinity to fermions and on the structure of the SBMS_4 algebra in terms of Lorentz representations.