On the all-order perturbative finiteness of the deformed N=4 SYM theory

Abstract

We prove that the chiral propagator of the deformed N=4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g. We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g^6.

LaTeX, 28 pages, 5 figures

References in corpus (1)

• On the perturbative chiral ring for marginally deformed N=4 SYM theories

Cited by in corpus (5)

• Proof of ultra-violet finiteness for a planar non-supersymmetric Yang-Mills theory
• Real versus complex beta-deformation of the N=4 planar super Yang-Mills theory
• Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory
• On beta-deformations and Noncommutativity
• Effective action of beta-deformed N = 4 SYM theory: Farewell to two-loop BPS diagrams