  We consider UV divergences for the on-shell planar gluon-gluon scattering
amplitudes in the gauge theory in arbitrary D-dimensions in the one-loop order.
The amplitudes are evaluated using the standard Feynman diagram technique for
several choices of external gluon polarizations. Using the Passarino - Veltman
reduction, the expansion in terms of the scalar master integrals is constructed
and their calculation is performed within dimensional regularization. The
resulting expressions are confronted with existing results for various cases,
including maximally supersymmetric theories in D=4, 6, 8, and 10 dimensions.
One finds that, contrary to the D=4 case, in D=6 one-loop UV divergences
cancel, while in D=8 and 10 the contributions of gauge, scalar and fermion
loops have the same sign.

High Energy Physics - Theory