Four Dimensional Conformal Supergravity From AdS Space
Vijay Balasubramanian, Eric Gimon, Djordje Minic, Joachim Rahmfeld
TL;DR
The paper shows that four-dimensional $N=1$ conformal supergravity naturally emerges on the boundary of five-dimensional AdS space when the bulk is governed by $N=2$ gauged supergravity, with radial diffeomorphisms providing the conformal boundary symmetry. Through the AdS/CFT correspondence, the conformal anomaly of the dual gauge theory (for example, $N=4$ SYM) holographically induces conformal gravity on the boundary, and the RG interpretation ties the boundary dynamics to bulk gravitational data. The leading logarithmic divergence of the boundary action reproduces the conformal gravity Lagrangian (constructed from $C^2 - E$), while finite Weyl-invariant pieces encode further bulk information; this framework extends to RS-type scenarios where Weyl symmetry is explicitly broken, yielding induced Poincaré gravity on a brane. The work also discusses the potential for dynamical conformal gravity on a finite-cutoff surface and outlines applications to holographic renormalization, SUSY boundary counterterms, and the embedding of conformal gravity within string-inspired holography.
Abstract
Exploring the role of conformal theories of gravity in string theory, we show that the minimal (N=2) gauged supergravities in five dimensions induce the multiplets and transformations of N=1 four dimensional conformal supergravity on the spacetime boundary. N=1 Poincare supergravity can be induced by explicitly breaking the conformal invariance via a radial cutoff in the 5d space. The AdS/CFT correspondence relates the maximal gauged supergravity in five dimensions to N=4 super Yang-Mills on the 4d spacetime boundary. In this context we show that the conformal anomaly of the gauge theory induces conformal gravity on the boundary of the space and that this theory, via the renormalization group, encapsulates the gravitational dynamics of the skin of asymptotically AdS spacetimes. Our results have several applications to the AdS/CFT correspondence and the Randall-Sundrum scenario.