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

TL;DR

This paper investigates the perturbative properties of the six-dimensional N=(1,1) supersymmetric Yang-Mills theory, revealing its unique divergence structure and exact Regge trajectory, challenging traditional views on nonrenormalizable theories.

Contribution

It provides the first detailed analysis of scattering amplitudes and divergence patterns in D=6 N=(1,1) SYM, highlighting its similarities to N=4 D=4 SYM and proposing a new perspective on nonrenormalizable theories.

Findings

No IR divergences on mass shell in D=6

Exact calculation of the Regge trajectory

Leading UV divergences suggest a finite sum

Abstract

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 N=4 D=4 SYM theory. The N=(1,1) D=6 SYM theory possesses similar properties but is nonrenomalizable and serves as a toy model for supergravity. We consider the on-shell four point scattering amplitude and analyze its perturbative expansion within the spin-helicity and superspace formalism. The integrands of the resulting diagrams coincide with those of the N=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.