N = 2 AdS4 supergravity, holography and Ward identities

• Published in: The journal of high energy physics Vol. 2021; no. 2
• Main Authors: Andrianopoli, L., Cerchiai, B. L., Matrecano, R., Miskovic, O., Noris, R., Olea, R., Ravera, L., Trigiante, M.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-02-2021; Springer Nature B.V
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Equations of motion; Field theory; Geometry; High energy physics; Holography; Identities; Mathematical analysis; Parameterization; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Spacetime; String Theory; Supergravity; Tensors; Supergravity Models; AdS-CFT Correspondence
• ISSN: 1029-8479
• DOI: 10.1007/JHEP02(2021)141

A
bstract
We develop in detail the holographic framework for an
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.