Absence of Three-Loop Four-Point Ultraviolet Divergences in $\mathcal{N}=4$ Supergravity

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Absence of Three-Loop Four-Point Ultraviolet Divergences in $N = 4$ Supergravity

Zvi Bern, Scott Davies, Tristan Dennen, and Yu-tin Huang

Phys. Rev. Lett. 108, 201301 – Published 15 May 2012

Abstract

We compute the coefficient of the potential three-loop four-point ultraviolet divergence in pure $N = 4$ supergravity and show that it vanishes, contrary to expectations from symmetry arguments. The recently uncovered duality between color and kinematics is used to greatly streamline the calculation. We comment on all-loop cancellations hinting at further surprises awaiting discovery at higher loops.

Received 16 February 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.201301

Authors & Affiliations

Zvi Bern^1,2, Scott Davies¹, Tristan Dennen¹, and Yu-tin Huang^1,3

¹Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547, USA
²Theory Division, Physics Department, CERN, CH—1211 Geneva 23, Switzerland
³School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA