On the amplitudes in $ \mathcal{N}=\left( {1,1} \right) $ D = 6 SYM

Abstract

We consider the on-shell amplitudes in $ \mathcal{N}=\left( {1,1} \right) $ SYM in D = 6 dimensions within the spinor helicity and on-shell superspace formalism. This leads to an effective and straightforward technique reducing the calculation to a set of scalar master integrals. As an example, the simplest four point amplitude is calculated in one and two loops in the planar limit. All answers are UV and IR finite and expressed in terms of logs and Polylogs of transcendentality level 2 at one loop, and 4 and 3 at two loops. The all loop leading logarithmical asymptotics at high energy is obtained which exhibits the Regge type behaviour. The intercept is calculated in the planar limit and is equal to $ \alpha (t)=1+\sqrt{{\frac{{g_{{Y\;M}}^2{N_c}\left| t \right|}}{{32{\pi^3}}}}} $ .