Conformal Invariance = Finiteness and Beta Deformed N=4 SYM Theory

Abstract

We claim that if by a choice of the couplings the theory can be made conformally invariant (vanishing of the beta functions) it is automatically finite and vice versa. This is demonstrated by explicit example in supersymmetric gauge theory. The formalism is then applied to the beta deformed $\mathcal{N}=4$ SYM theory and it is shown that the requirement of conformal invariance = finiteness can be achieved for any complex parameter of deformations.

15 pages, Latex, 1 figure axodraw style

References in corpus (12)

• Gauge Theory Correlators from Non-Critical String Theory
• 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
• Novel Local CFT and Exact Results on Perturbations of N=4 Super Yang Mills from AdS Dynamics
• Beauty and the Twist: The Bethe Ansatz for Twisted N=4 SYM
• Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
• On Exactly Marginal Deformations of N=4 SYM and Type IIB Supergravity on AdS_5 * S^5
• Amplitudes in the beta-deformed Conformal Yang-Mills
• New results in the deformed N=4 SYM theory
• Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real
• Generalizations of Lunin-Maldacena transformation on the $AdSsub5xSsup5$ background
• On the all-order perturbative finiteness of the deformed N=4 SYM theory

Cited by in corpus (9)

• Superconformal indices of $\mathcal{N}=4$ SYM field theories
• Conformal Invariance in the Leigh-Strassler deformed N=4 SYM Theory
• $\beta$-deformation for matrix model of M-theory
• Yangians in Deformed Super Yang-Mills Theories
• Nonanticommutative U(1) SYM theories: Renormalization, fixed points and infrared stability
• Supergraphs and the cubic Leigh-Strassler model
• Matrix Model and beta-deformed N=4 SYM
• Bilocal phase operators in beta-deformed super Yang-Mills
• Dynamical SUSY Breaking and the Beta-Deformation