Local supersymmetry and the square roots of Bondi-Metzner-Sachs supertranslations

Abstract

Super-BMS${}_4$ algebras -- also called BMS${}_4$ superalgebras -- are graded extensions of the BMS${}_4$ algebra. They can be of two different types: they can contain either a finite number or an infinite number of fermionic generators. We show in this letter that, with suitable boundary conditions on the graviton and gravitino fields at spatial infinity, supergravity on asymptotically flat spaces possesses as superalgebra of asymptotic symmetries a (nonlinear) super-BMS${}_4$ algebra containing an infinite number of fermionic generators, which we denote SBMS${}_4$. These boundary conditions are not only invariant under SBMS${}_4$, but also lead to a fully consistent canonical description of the supersymmetries, which have in particular well-defined Hamiltonian generators that close according to the nonlinear SBMS${}_4$ algebra. One finds in particular that the graded brackets between the fermionic generators yield all the BMS${}_4$ supertranslations, of which they provide therefore "square roots".

arXiv comment7 pages, no figures

References in corpus (26)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• Aspects of the BMS/CFT correspondence
• Symmetries of asymptotically flat 4 dimensional spacetimes at null infinity revisited
• Asymptotic Dynamics and Asymptotic Symmetries of Three-Dimensional Extended AdS Supergravity
• BMS Group at Spatial Infinity: the Hamiltonian (ADM) approach
• Null infinity, the BMS group and infrared issues
• A Critique of Pure String Theory: Heterodox Opinions of Diverse Dimensions
• The BMS4 algebra at spatial infinity
• Extended Super BMS Algebra of Celestial CFT
• The Asymptotic Behavior of Massless Fields and the Memory Effect
• Hamiltonian structure and asymptotic symmetries of the Einstein-Maxwell system at spatial infinity
• Relaxing the Parity Conditions of Asymptotically Flat Gravity
• Peeling or not peeling -- is that the question ?
• A new class of obstructions to the smoothness of null infinity
• Residual Local Supersymmetry and the Soft Gravitino
• On the structure and applications of the Bondi-Metzner-Sachs group
• Results of the classification of superconformal algebras in two dimensions
• The Case Against Smooth Null Infinity I: Heuristics and Counter-Examples
• Massive Celestial Fermions
• Asymptotic realization of the super-BMS algebra at spatial infinity
• Asymptotic symmetries of Yang-Mills fields in Hamiltonian formulation
• Asymptotic structure of the Rarita-Schwinger theory in four spacetime dimensions at spatial infinity
• The Case Against Smooth Null Infinity II: A Logarithmically Modified Price's Law
• Asymptotic structure of the Pauli-Fierz theory in four spacetime dimensions
• Asymptotic symmetries of scalar electrodynamics and of the abelian Higgs model in Hamiltonian formulation

Cited by in corpus (13)

• Logarithmic supertranslations and supertranslation-invariant Lorentz charges
• Celestial Holography: Lectures on Asymptotic Symmetries
• The Bondi-Metzner-Sachs group in five spacetime dimensions
• Conformally Soft Fermions
• Asymptotic structure of the gravitational field in five spacetime dimensions: Hamiltonian analysis
• Supersymmetrization of deformed BMS algebras
• Radiative Asymptotic Symmetries of 3D Einstein-Maxwell Theory
• Asymptotic $\mathcal{O}(r)$ gauge symmetries and gauge-invariant Poincaré generators in higher spacetime dimensions
• A novel supersymmetric extension of BMS symmetries at null infinity
• Conserved asymptotic charges for any massless particle
• BRST BMS4 Symmetry and its Cocycles from Horizontality Conditions
• On the nature of Bondi-Metzner-Sachs transformations
• On the geometric approach to the boundary problem in supergravity