High Energy Behavior in Maximally Supersymmetric Gauge Theories in Various Dimensions

Abstract

Maximally supersymmetric field theories in various dimensions are believed to possess special properties due to extended supersymmetry. In four dimensions they are free from UV divergences but are IR divergent on shell, in higher dimensions, on the contrary, they are IR finite but UV divergent. In what follows we consider the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theory in the planar limit within the spinor-helicity and on shell supersymmetric formalism. We study the UV divergences and demonstrate how one can sum them over all orders of PT. Analyzing the R-operation, we obtain the recursive relations and derive differential equations that sum all leading, subleading, etc., divergences in all loops generalizing the standard RG formalism for the case of nonrenormalizable interactions. We then perform the renormalization procedure which differs from the ordinary one in that the renormalization constant becomes the operator depending on kinematics. Solving the obtained RG equations for particular sets of diagrams analytically and for the general case numerically, we analyze their high energy behaviour and find out that while each term of PT increases as a power of energy, the total sum behaves differently: in D=6 two partial amplitudes decrease with energy and the third one increases exponentially, while in D=8 and 10 the amplitudes possess an infinite number of periodic poles at finite energy.

Non-renormalizable Interactions: A Self-Consistency Manifesto

“…In renormalizable theories these relations are known as pole equations (within dimensional regularization) and are governed by the renormalization group [12]. The same is true, though technically is more complicated, in any local theory, as we have demonstrated in [13]- [15] (see also review in [11]). We remind here some features of this procedure.…”

“…We discussed some features of the scheme dependence in [11]. It is governed by the finite renormalization (23) where z acts as an operator in the above mentioned sense.…”