Extension of the Poincar´e group with half-integer spin generators :hypergravity, asymptotically flat structure and energy bounds

Abstract

This thesis presents a novel extension of the Poincar´e group with half-integer spin generators and a reformulation of hypergravity. This theory describes fermionic higher spin fields minimally coupled to gravity in three spacetime dimensions. The subsequent studies of its asymptotically flat structure and energy bounds are also carried out. We start our discussion in the case of three spacetime dimensions, where it is shown that the theory of hypergravity can be reformulated in order to incorporate this structure as its local gauge symmetry. Since the algebra admits a nontrivial Casimir operator, the theory can be described in terms of gauge fields associated to the extension of the Poincar´e group with a Chern-Simons action. We also show that the Poincar´e group can be extended with arbitrary half-integer spin generators for d ! 3 dimensions. The asymptotic structure of three-dimensional hypergravity is also analyzed. In the case of gravity minimally coupled to a spin-5/2 field, a consistent set of boundary conditions is proposed, being wide enough so as to accommodate a generic choice of chemical potentials associated to the global charges. The algebra of the canonical generators of the asymptotic symmetries is given by a hypersymmetric nonlinear extension of BMS3. It is shown that the asymptotic symmetry algebra can be recovered from a subset of a suitable limit of the direct sum of the W(2,4) algebra with its hypersymmetric extension. The presence of hypersymmetry generators allows to construct bounds for the energy, which turn out to be nonlinear and saturate for spacetimes that admit globally-defined Killing vector-spinors. The null orbifold or Minkowski spacetime can then be seen as the corresponding ground state in the case of fermions that fulfill periodic or antiperiodic boundary conditions, respectively. The hypergravity theory is also explicitly extended so as to admit parity-odd terms in the action.