Real versus complex beta-deformation of the N=4 planar super Yang-Mills theory

Abstract

This is a sequel of our paper hep-th/0606125 in which we have studied the {\cal N}=1 SU(N) SYM theory obtained as a marginal deformation of the {\cal N}=4 theory, with a complex deformation parameter βand in the planar limit. There we have addressed the issue of conformal invariance imposing the theory to be finite and we have found that finiteness requires reality of the deformation parameter β. In this paper we relax the finiteness request and look for a theory that in the planar limit has vanishing beta functions. We perform explicit calculations up to five loop order: we find that the conditions of beta function vanishing can be achieved with a complex deformation parameter, but the theory is not finite and the result depends on the arbitrary choice of the subtraction procedure. Therefore, while the finiteness condition leads to a scheme independent result, so that the conformal invariant theory with a real deformation is physically well defined, the condition of vanishing beta function leads to a result which is scheme dependent and therefore of unclear significance. In order to show that these findings are not an artefact of dimensional regularization, we confirm our results within the differential renormalization approach.

arXiv comment18 pages, 7 figures; v2: one reference added; v3: JHEP published version

References in corpus (17)

• 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
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• Deformations of N=4 SYM and integrable spin chain models
• Scheme dependence and the NSVZ $\beta$-function
• Exact results in planar N=1 superconformal Yang-Mills theory
• Dipole Deformations of N=1 SYM and Supergravity backgrounds with U(1) X U(1) global symmetry
• On spin chains and field theories
• Amplitudes in the beta-deformed Conformal Yang-Mills
• Systematic Differential Renormalization to All Orders
• New results in the deformed N=4 SYM theory
• Proof of all-order finiteness for planar beta-deformed Yang-Mills
• Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real
• Effective action of beta-deformed N=4 SYM theory and AdS/CFT
• A Cutoff Procedure and Counterterms for Differential Renormalization
• On the all-order perturbative finiteness of the deformed N=4 SYM theory
• Differential Renormalization, the Action Principle and Renormalization Group Calculations

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• Conformal Invariance in the Leigh-Strassler deformed N=4 SYM Theory
• Gluon Scattering in Deformed N=4 SYM
• $\beta$-deformation for matrix model of M-theory
• Yangians in Deformed Super Yang-Mills Theories
• Conformal invariance and finiteness theorems for non-planar beta-deformed N=4 SYM theory
• Four-loop anomalous dimensions in Leigh-Strassler deformations
• Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability
• Structure constants of $\beta$ deformed super Yang-Mills
• Supergraphs and the cubic Leigh-Strassler model
• Two loop Kahler potential in beta-deformed N=4 SYM theory
• Bilocal phase operators in beta-deformed super Yang-Mills
• Dynamical SUSY Breaking and the Beta-Deformation