On divergences in non-minimal N=4 conformal supergravity

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Title: On divergences in non-minimal N=4 conformal supergravity
Authors: Tseytlin, AA
Item Type: Journal Article
Abstract: We review the question of quantum consistency of $ \newcommand{\N}{{{\mathcal N}}} \N=4$ conformal supergravity in 4 dimensions. The UV divergences and anomalies of the standard ('minimal') conformal supergravity where the complex scalar $ \newcommand{\vp}{\varphi} \vp$ is not coupled to the Weyl graviton kinetic term can be cancelled by coupling this theory to $ \newcommand{\N}{{{\mathcal N}}} \N=4$ super Yang–Mills with gauge group of dimension 4. The same turns out to be true also for the 'non-minimal' $ \newcommand{\N}{{{\mathcal N}}} \N=4$ conformal supergravity with the action (recently constructed (Butter et al 2017 Phys. Rev. Lett. 118 081602)) depending on an arbitrary holomorphic function $ \newcommand{\vp}{\varphi} f(\vp)$ . The special case of the 'non-minimal' conformal supergravity with $ \newcommand{\vp}{\varphi} f= {\rm e}^{2\vp}$ 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' $f=1$ case by coupling the theory to four $ \newcommand{\N}{{{\mathcal N}}} \N=4$ vector multiplets.
Issue Date: 1-Dec-2017
Date of Acceptance: 9-Oct-2017
ISSN: 1751-8113
Publisher: IOP Publishing
Journal / Book Title: Journal of Physics A: Mathematical and Theoretical
Volume: 50
Issue: 48
Copyright Statement: © 2017 IOP Publishing Ltd. This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The definitive publisher authenticated version is available online at
Sponsor/Funder: Science and Technology Facilities Council (STFC)
Science and Technology Facilities Council (STFC)
Science and Technology Facilities Council (STFC)
Funder's Grant Number: ST/G000743/1
Keywords: Science & Technology
Physical Sciences
Physics, Multidisciplinary
Physics, Mathematical
conformal supergravity
conformal anomalies
super Yang-Mills
01 Mathematical Sciences
02 Physical Sciences
Mathematical Physics
Publication Status: Published
Article Number: 48LT01
Online Publication Date: 2017-10-09
Appears in Collections:Physics
Theoretical Physics
Faculty of Natural Sciences

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