Research in the Particle Theory group

(David Dunbar, Warren Perkins)

There has been remarkable progress in understanding gauge theories with extended supersymmetry, with many relations having been discovered between their perturbative expansion and topological string theory, dual superconformal invariance, Yangian symmetries and integrability. In contrast, in perturbative supergravity the corresponding dualities and symmetries are unknown. However, the explicit perturbative expansion for N = 8 supergravity mirrors that of N = 4 gauge theory: specifically, the “No-Triangle” property holds for any one-loop amplitude, and explicit amplitudes beyond one loop give the same ultra-violet behaviour as maximally supersymmetric Yang-Mills. There is clearly an undiscovered symmetry structure in SUSY Yang-Mills and supergravity which is being revealed by these amplitudes. This raises the intriguing possibility that N = 8 and indeed other supergravity theories are finite. Much of our current research is aimed at exploring this possibility.

Dunbar was one of the pioneers of unitarity techniques for unlocking the perturbative structure of quantum field theories. The synthesis of unitarity with the on-shell recursion techniques developed by Britto, Cachazo, Feng and Witten has led to a fascinating and very fruitful period for perturbation theory. Dunbar and Perkins have pursued the development of these new calculational techniques and have shed light on the hidden symmetries and structures of amplitudes. Focusing on supergravity theories with less than maximal symmetry, we made the striking prediction, subsequently confirmed by explicit calculations by Bern and collaborators, that the three-loop divergence in N = 4 supergravity would cancel.