Conformal invariance from non-conformal gravity

TL;DR

The paper investigates whether classically conformal four-dimensional theories can arise from a non-conformal gravity framework. It provides an explicit existence proof by deriving $N=4$ super Yang–Mills theory with gauge group $G$ from non-conformal gauged $N=4$ supergravity in the flat-space limit $\kappa\to 0$, recovering the standard $N=4$ YM interactions and a sextet of scalars while ensuring proper decoupling of gravity. It emphasizes that a UV-finite underlying theory of quantum gravity would be essential for this scheme and that mass scales would have to emerge from quantum gravitational effects that mimic conformal anomalies, not from classical gravity alone. The authors conjecture that, in a UV-finite gravity theory, anomalous logarithmic corrections depending on $\log(\kappa\phi)$ could replace the Coleman–Weinberg mechanism, with an anomalous Ward identity $T^{\mu}{}_{\mu} = \beta(\hat{\lambda}(\kappa\phi))\phi^4 + Z(\hat{\lambda}(\kappa\phi))\partial_\mu\phi\partial^\mu\phi$ encoding how conformal symmetry is broken, offering a potential gravity-induced route to the observed hierarchy.

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.