Four Dimensional Conformal Supergravity From AdS Space

TL;DR

This paper investigates how five-dimensional gauged supergravity theories induce four-dimensional conformal supergravity on the boundary of AdS space, revealing connections between conformal anomalies, holography, and gravitational dynamics.

Contribution

It demonstrates the derivation of 4D conformal supergravity from 5D gauged supergravity within the AdS/CFT framework, highlighting the role of conformal anomalies and boundary conditions.

Findings

Induces 4D conformal supergravity from 5D gauged supergravity.

Shows conformal anomaly leads to boundary conformal gravity.

Connects gravitational dynamics with renormalization group flow.

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.