TY - JOUR

T1 - Asymptotically flat structure of hypergravity in three spacetime dimensions

AU - Fuentealba, Oscar

AU - Matulich, Javier

AU - Troncoso, Ricardo

N1 - Publisher Copyright:
© 2015, The Author(s).

PY - 2015/10/1

Y1 - 2015/10/1

N2 - Abstract: The asymptotic structure of three-dimensional hypergravity without cosmological constant is 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. It is then shown that the asymptotic symmetry algebra includes an additional central charge, being proportional to the coupling of the Lorentz-Chern-Simons form. The generalization of these results in the case of gravity minimally coupled to arbitrary half-integer spin fields is also carried out. The hypersymmetry bounds are found to be given by a suitable polynomial of degree s+12$$ s+\frac{1}{2} $$ in the energy, where s is the spin of the fermionic generators.

AB - Abstract: The asymptotic structure of three-dimensional hypergravity without cosmological constant is 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. It is then shown that the asymptotic symmetry algebra includes an additional central charge, being proportional to the coupling of the Lorentz-Chern-Simons form. The generalization of these results in the case of gravity minimally coupled to arbitrary half-integer spin fields is also carried out. The hypersymmetry bounds are found to be given by a suitable polynomial of degree s+12$$ s+\frac{1}{2} $$ in the energy, where s is the spin of the fermionic generators.

KW - Classical Theories of Gravity

KW - Conformal and W Symmetry

KW - Gauge-gravity correspondence

KW - Higher Spin Symmetry

UR - http://www.scopus.com/inward/record.url?scp=84943173849&partnerID=8YFLogxK

U2 - 10.1007/JHEP10(2015)009

DO - 10.1007/JHEP10(2015)009

M3 - Article

AN - SCOPUS:84943173849

SN - 1126-6708

VL - 2015

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 9

ER -