Challenges of D=6 N = (1,1) SYM theory

Maximally supersymmetric Yang-Mills theories have several remarkable properties, among which are the cancellation of UV divergences, factorization of higher loop corrections and possible integrability. Much attention has been attracted to the Ar = 4 D = 4 SYM theory. The Ar = (1, 1) D = 6 SYM theory possesses similar properties but is nonrenormalizable and serves as a toy model for supergravity. We consider the on-shell four point scattering amplitude and analyze its perturbative expansion within the spinhelicity and superspace formalism. The integrands of the resulting diagrams coincide with those of the Ar = 4 D = 4 SYM and obey the dual conformal invariance. Contrary to 4 dimensions, no IR divergences on mass shell appear. We calculate analytically the leading logarithmic asymptotics in all loops. Their summation leads to a Regge trajectory which is calculated exactly. The leading powers of s are calculated up to six loops. Their summation is performed numerically and leads to a smooth function of s. The leading UV divergences are calculated up to 5 loops. The result suggests the geometrical progression which ends up in a finite expression. This leads us to a radical point of view on nonrenormalizable theories. (C) 2014 The Authors. Published by Elsevier B.V.