Conformal invariance from non-conformal gravity

TL;DR

This paper explores how conformally invariant models in four dimensions can originate from non-conformal Einstein gravity, demonstrating a derivation of N=4 super Yang-Mills theory from non-conformal supergravity.

Contribution

It provides a theoretical framework showing the emergence of conformal invariance from non-conformal gravity and derives N=4 super Yang-Mills theory as a flat space limit.

Findings

Derivation of N=4 super Yang-Mills from non-conformal supergravity.

Highlighting the role of quantum gravity in mass generation and conformal anomalies.

Discussion of UV finiteness implications for quantum gravity theories.

Abstract

We discuss the conditions under which classically conformally invariant models in four dimensions can arise out of non-conformal (Einstein) gravity. As an `existence proof' that this is indeed possible we show how to derive N=4 super Yang Mills theory with any compact gauge group G from non-conformal gauged N=4 supergravity as a special flat space limit. We stress the role that the anticipated UV finiteness of the (so far unknown) underlying theory of quantum gravity would have to play in such a scheme, as well as the fact that the masses of elementary particles would have to arise via quantum gravitational effects which mimic the conformal anomalies of standard (flat space) UV divergent quantum field theory.