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.

arXiv commentLaTeX, 28 pages, 5 figures

References in corpus (25)

• Deforming field theories with $U(1)\times U(1)$ global symmetry and their gravity duals
• Exactly Marginal Operators and Duality in Four Dimensional N=1 Supersymmetric Gauge Theory
• Lax Pair for Strings in Lunin-Maldacena Background
• Holomorphy, Rescaling Anomalies and Exact beta Functions in Supersymmetric Gauge Theories
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
• Marginal and Relevant Deformations of N=4 Field Theories and Non-Commutative Moduli Spaces of Vacua
• Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
• Discrete Torsion, AdS/CFT and duality
• On Exactly Marginal Deformations of N=4 SYM and Type IIB Supergravity on AdS_5 * S^5
• Bonus Symmetry and the Operator Product Expansion of N=4 Super-Yang-Mills
• $N=1$ supersymmetry and the three loop anomalous dimension for the chiral superfield
• On the logarithmic behaviour in N=4 SYM theory
• Exact results in planar N=1 superconformal Yang-Mills theory
• Amplitudes in the beta-deformed Conformal Yang-Mills
• Two-point correlators in the beta-deformed N=4 SYM at the next-to-leading order
• Comments on the beta-deformed N=4 SYM Theory
• New results in the deformed N=4 SYM theory
• Emergent geometry from q-deformations of N=4 super Yang-Mills
• On the perturbative chiral ring for marginally deformed N=4 SYM theories
• Surprises from the Resolution of Operator Mixing in N = 4 SYM
• Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real
• Operator mixing in N=4 SYM: The Konishi anomaly revisited
• Generalizations of Lunin-Maldacena transformation on the $AdSsub5xSsup5$ background
• Some Systematics of the Coupling Constant Dependence of N=4 Yang-Mills

Cited by in corpus (16)

• Proof of all-order finiteness for planar beta-deformed Yang-Mills
• Proof of ultra-violet finiteness for a planar non-supersymmetric Yang-Mills theory
• The Leigh-Strassler Deformation and the Quest for Integrability
• Quantum Symmetries and Marginal Deformations
• Real versus complex beta-deformation of the N=4 planar super Yang-Mills theory
• Conformal Invariance in the Leigh-Strassler deformed N=4 SYM Theory
• $\beta$-deformation for matrix model of M-theory
• Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory
• Chiral primaries in the Leigh-Strassler deformed N=4 SYM -- a perturbative study
• On beta-deformations and Noncommutativity
• Effective action of beta-deformed N = 4 SYM theory: Farewell to two-loop BPS diagrams
• On the non-planar beta-deformed N=4 super-Yang-Mills theory
• Studies of low-energy effective actions in supersymmetric field theories
• Supergraphs and the cubic Leigh-Strassler model
• Two loop Kahler potential in beta-deformed N=4 SYM theory
• Matrix Model and beta-deformed N=4 SYM