Conformal invariance of the planar beta-deformed N=4 SYM theory requires beta real

TL;DR

This paper investigates a marginal deformation of N=4 SYM theory, demonstrating that conformal invariance at large N requires the deformation parameter beta to be real, thus constraining the theory's parameter space.

Contribution

It establishes that conformal invariance in the planar beta-deformed N=4 SYM theory necessitates a real deformation parameter, providing a key condition for the theory's consistency.

Findings

Finiteness of the theory requires beta to be real.

Conformal invariance constrains the complex deformation parameter.

Large N perturbative analysis supports the reality condition.

Abstract

We study the \cal{N}=1 SU(N) SYM theory which is a marginal deformation of the \cal{N}=4 theory, with a complex deformation parameter \beta. We consider the large N limit and study perturbatively the conformal invariance condition. We find that finiteness requires reality of the deformation parameter \beta.