Summation of all-loop UV divergences in maximally supersymmetric gauge theories

A bstract We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished pro...

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Bibliographic Details
Published in:The journal of high energy physics 2016-12, Vol.2016 (12), p.1-18, Article 154
Main Authors: Borlakov, A. T., Kazakov, D. I., Tolkachev, D. M., Vlasenko, D. E.
Format: Article
Language:English
Subjects:
Cancellation
Classical and Quantum Gravitation
Differential equations
Elementary Particles
Gauge theory
High energy physics
Mathematical analysis
Perturbation theory
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Regularization
Relativity Theory
Scattering amplitude
String Theory
Supersymmetry
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Summary:A bstract We consider the leading and subleading UV divergences for the four-point on-shell scattering amplitudes in D=6,8,10 supersymmetric Yang-Mills theories in the planar limit. These theories belong to the class of maximally supersymmetric gauge theories and presumably possess distinguished properties beyond perturbation theory. In the previous works, we obtained the recursive relations that allow one to get the leading and subleading divergences in all loops in a pure algebraic way. The all loop summation of the leading divergences is performed with the help of the differential equations which are the generalization of the RG equations for non-renormalizable theories. Here we mainly focus on solving and analyzing these equations. We discuss the properties of the obtained solutions and interpretation of the results. The key issue is that the summation of infinite series for the leading and the subleading divergences does improve the situation and does not allow one to remove the regularization and obtain the finite answer. This means that despite numerous cancellations of divergent diagrams these theories remain non-renormalizable.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP12(2016)154