Arxiv:2010.02119V2 [Hep-Th] 13 Jan 2021
=2 AdS4 supergravity, holography and Ward N identities L. Andrianopoli1,2,3, B.L. Cerchiai1,2,3,4, R. Matrecano1,2, O. Miskovic5, R. Noris1,2, R. Olea6, L. Ravera1,2, M. Trigiante1,2,3 1 DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Turin, Italy 2 Istituto Nazionale di Fisica Nucleare (INFN) Sezione di Torino, Italy 3 Arnold - Regge Center, Via P. Giuria 1, 10125 Torino, Italy 4 Centro Ricerche “Enrico Fermi”, Piazza del Viminale, 1, I-00184 Rome, Italy 5 Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4059, Valparaíso, Chile 6 Departamento de Ciencias Físicas, Universidad Andres Bello, Sazié 2212, Piso 7, Santiago, Chile Abstract We develop in detail the holographic framework for an = 2 pure AdS supergravity model N 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 superconformal 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.
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