SIMILARITIES OF GAUGE AND GRAVITY AMPLITUDES

Perturbative gauge theory and gravity in four dimensions are quite dissimilar from adynamical viewpoint. Gauge theory (e.g. pure Yang-Mills theory) is a renormalisabletheory that is strongly coupled in the infrared and asymptotically free in the ultraviolet.Gravity on the other hand is a weakly coupled theory in the infrared but stronglycoupled in the ultraviolet. By power counting, gravity in four dimensions is potentiallya non-renormalisable theory. Pure gravity scattering amplitudes are finite at one-loopwith the first divergence occurring at two-loops[1].Supersymmetry generally softens the UV behaviour in a quantum field theory. Forexample, maximally supersymmetric Yang-Mills is a finite theory[2] and supergravitytheories have a finite S-matrix until at least three loops[3]. Although four-dimensionalpower counting and counter-term arguments suggest that supergravity theories are non-renormalisable[4] this has, so far, not been tested by direct computations. Argumentsbased on power counting within unitary cuts suggest that the first counter term inmaximal supergravity[5] is expected at five loops[6, 7].Recently, initiated by the duality between gauge theories and a twister string the-ory[8], there has been much progress in the computation of amplitudes in gauge theory.In this talk we discuss how these ideas may be applied to gravity calculations and theresults thereof. We will first review the recent progress in computing physical on-shelltree amplitudes for gravity theories particularly focusing on the on-shell recursion rela-tions[9, 10] and the MHV-vertex construction[11, 12, 13, 14, 15]. Later we will discussone-loop amplitudes. A surprising result is that the one-loop amplitudes of N = 4 SYMand N = 8 supergravity[16, 17] occur to be expressible in terms of scalar box integralfunctions - despite the expectation from power counting. Supergravity multi-loop am-plitudes are not directly addressed, however, the structure of amplitudes at tree-leveland one-loop have, through factorisation and unitarity, important consequences on thestructure of higher loop amplitudes.