Journal of High Energy Physics (Feb 2021)

N $$ \mathcal{N} $$ = 2 AdS4 supergravity, holography and Ward identities

  • L. Andrianopoli,
  • B. L. Cerchiai,
  • R. Matrecano,
  • O. Miskovic,
  • R. Noris,
  • R. Olea,
  • L. Ravera,
  • M. Trigiante

DOI
https://doi.org/10.1007/JHEP02(2021)141
Journal volume & issue
Vol. 2021, no. 2
pp. 1 – 70

Abstract

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Abstract We develop in detail the holographic framework for an N $$ \mathcal{N} $$ = 2 pure AdS supergravity model in four dimensions, including all the contributions from the fermionic fields and adopting the Fefferman-Graham parametrization. We work in the first order formalism, where the full superconformal structure can be kept manifest in principle, even if only a part of it is realized as a symmetry on the boundary, while the remainder has a non-linear realization. Our study generalizes the results presented in antecedent literature and includes a general discussion of the gauge-fixing conditions on the bulk fields which yield the asymptotic symmetries at the boundary. We construct the corresponding super- conformal currents and show that they satisfy the related Ward identities when the bulk equations of motion are imposed. Consistency of the holographic setup requires the super- AdS curvatures to vanish at the boundary. This determines, in particular, the expression of the super-Schouten tensor of the boundary theory, which generalizes the purely bosonic Schouten tensor of standard gravity by including gravitini bilinears. The same applies to the superpartner of the super-Schouten tensor, the conformino. Furthermore, the vanishing of the supertorsion poses general constraints on the sources of the three-dimensional boundary conformal field theory and requires that the super-Schouten tensor is endowed with an antisymmetric part proportional to a gravitino-squared term.

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