Generalised cusp anomalous dimension in beta-deformed super Yang Mills theory

TL;DR

This paper investigates the cusp anomalous dimension in beta-deformed N=4 super Yang-Mills theory, deriving expressions at weak and strong coupling, and introduces an effective angle to relate deformed and undeformed theories, revealing a BPS-like condition.

Contribution

It introduces an effective angle in the internal space to relate the deformed theory's cusp anomalous dimension to the undeformed N=4 sYM, extending the understanding across coupling regimes.

Findings

Cusp anomalous dimension matches N=4 sYM at weak coupling up to two loops.

An effective angle ff} relates deformed and undeformed theories at strong coupling.

A BPS-like condition nullifies the cusp anomalous dimension when satisfied.

Abstract

In this work we study the cusp anomalous dimension of the marginally deformed N=4 sYM theory. We find the expression of the cusp anomalous dimension both at the weak and strong coupling limits. On the gravity side we partially map the system of equations to that of undeformed N=4 sYM, by defining in the internal space an effective angle \Delta \theta_{eff} which depends on the deformation parameter. The cusp anomalous dimension then can be read from that of the N=4 sYM theory, by using this effective angle instead of the usual angle of the undeformed 5-sphere. In the weak coupling regime we find no beta dependence up to two loops. Based on these results we conjecture that for any value of lambda, the cusp anomalous dimension is given by the N=4 sYM result using the coupling dependent effective angle. As a consequence of this, we derive a BPS-like condition between the angle of the AdS space and the \Delta \theta_{eff} of the deformed sphere which when satisfied, nullifies the cusp anomalous dimension.