Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions

TL;DR

This paper investigates the ultraviolet divergences in maximally supersymmetric Yang-Mills theories across six, eight, and ten dimensions, providing loop calculations, recursive relations, and insights into the series summation and fixed points.

Contribution

It systematically analyzes divergences in high-dimensional supersymmetric gauge theories using novel recursive and summation techniques, extending previous understanding of their ultraviolet behavior.

Findings

Divergences start at 3 loops in D=6 and at 1 loop in D=8,10.

Derived recursive relations for divergence polynomials at any perturbation order.

Identified fixed points in the summed perturbation series with potential stability implications.

Abstract

The main aim of this paper is to study the scattering amplitudes in gauge field theories with maximal supersymmetry in dimensions D=6,8 and 10. We perform a systematic study of the leading ultraviolet divergences using the spinor helicity and on-shell momentum superspace framework. In D=6 the first divergences start at 3 loops and we calculate them up to 5 loops, in D=8,10 the first divergences start at 1 loop and we calculate them up to 4 loops. The leading divergences in a given order are the polynomials of Mandelstam variables. To be on the safe side, we check our analytical calculations by numerical ones applying the alpha-representation and the dedicated routines. Then we derive an analog of the RG equations for the leading pole that allows us to get the recursive relations and construct the generating procedure to obtain the polynomials at any order of (perturbation theory) PT. At last, we make an attempt to sum the PT series and derive the differential equation for the infinite sum. This equation possesses a fixed point which might be stable or unstable depending on the kinematics. Some consequences of these fixed points are discussed.