On divergences in non-minimal N=4 conformal supergravity

Understand

We review the question of quantum consistency of N=4 conformal supergravity in 4 dimensions.

• The UV divergences and anomalies of the standard ("minimal") conformal supergravity where the complex scalar $\phi$ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to N=4 super Yang-Mills with gauge group of dimension 4.
• The same turns out to be true also for the "non-minimal" N=4 conformal supergravity with the action (recently constructed in arXiv:1609.09083) depending on an arbitrary holomorphic function $f(\phi)$.
• The special case of the "non-minimal" conformal supergravity with $f= e^{2\phi}$ appears in the twistor-string theory.