Weyl vs. Conformal

TL;DR

This paper discusses the limitations of coupling conformally invariant theories in flat spacetime to gravity while maintaining Weyl invariance, highlighting fundamental constraints in theoretical physics.

Contribution

It demonstrates that not all conformally invariant theories can be coupled to gravity in a Weyl invariant manner, revealing a key limitation.

Findings

Certain conformally invariant theories cannot be Weyl coupled to gravity

Weyl invariance cannot always be preserved in gravitational coupling

Highlights fundamental constraints in conformal and gravitational theories

Abstract

In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.