Vanishing One-Loop <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>β</mi></math></span> Function in Gauged <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>N</mi><mo>></mo><mn></mn><mn>4</mn><mn></mn></math></span> Supergravity

S. M. Christensen; M. J. Duff; G. W. Gibbons; M. Roček

doi:10.1103/PhysRevLett.45.161

Vanishing One-Loop $β$ Function in Gauged $N > 4$ Supergravity

S. M. Christensen, M. J. Duff, G. W. Gibbons, and M. Roček

Phys. Rev. Lett. 45, 161 – Published 21 July 1980

Abstract

In O $(N)$ extended supergravity theories, the usual arguments for one-loop finiteness (modulo topological terms) cease to apply when the internal symmetry is gauged because of the appearance of a cosmological constant related to the gauge coupling $e$ . For $N <~ 4$ , we find that infinite renormalizations are required. Remarkably, the particle content of theories with $N > 4$ results in a cancellation of these infinities, implying, in particular a vanishing one-loop $β (e)$ function.

Received 4 April 1980

DOI:https://doi.org/10.1103/PhysRevLett.45.161

Authors & Affiliations

S. M. Christensen

Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, California 93106

M. J. Duff

Physics Department, Imperial College, London SW7 2AZ, United Kingdom

G. W. Gibbons^*

Institute for Theoretical Physics, University of California at Santa Barbara, Santa Barbara, California 93106, and Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 9EW, United Kingdom

M. Roček