The Boundary Multiplet of N=4 SU(2)xU(1) Gauged Supergravity on Asymptotically-AdS_5

TL;DR

This paper analyzes N=4 SU(2)xU(1) gauged supergravity on asymptotically-AdS_5, deriving the boundary N=2 Weyl multiplet and computing the Weyl anomaly of the dual 4D superconformal field theory.

Contribution

It identifies the boundary multiplet structure from bulk supergravity and connects it to N=2 superconformal symmetry, extending the AdS/CFT correspondence analysis.

Findings

Boundary components form the N=2 Weyl multiplet.

Residual bulk symmetries act as 4D superconformal transformations.

Calculated the Weyl anomaly for the dual SCFT.

Abstract

We consider N=4 SU(2)xU(1) gauged supergravity on asymptotically-AdS_5 backgrounds. By a near-boundary analysis we determine the boundary-dominant components of the bulk fields from their partially gauge-fixed field equations. Subdominant components are projected out in the boundary limit and we find a reduced set of boundary fields, constituting the N=2 Weyl multiplet. The residual bulk symmetries are found to act on the boundary fields as four-dimensional diffeomorphisms, N=2 supersymmetry and (super-)Weyl transformations. This shows that the on-shell N=4 supergravity multiplet yields the N=2 Weyl multiplet on the boundary with the appropriate local N=2 superconformal transformations. Building on these results we use the AdS/CFT conjecture to calculate the Weyl anomaly of the dual four-dimensional superconformal field theories in a generic bosonic N=2 conformal supergravity background.