On divergences in non-minimal conformal supergravity

Abstract

We review the question of quantum consistency of conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard (‘minimal’) conformal supergravity where the complex scalar is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to super Yang–Mills with gauge group of dimension 4. The same turns out to be true also for the ‘non-minimal’ conformal supergravity with the action (recently constructed (Butter et al 2017 Phys. Rev. Lett. 118 081602)) depending on an arbitrary holomorphic function . The special case of the ‘non-minimal’ conformal supergravity with appears in the twistor-string theory. We show that divergences and anomalies do not depend on the form of the function f and thus can be cancelled just as in the ‘minimal’ case by coupling the theory to four vector multiplets.