Wilson loops and anomalous dimensions in cascading theories

TL;DR

This paper calculates the anomalous dimensions of twist two operators in the cascading Klebanov-Strassler theory using light-like Wilson loops and AdS/CFT, revealing a scale-dependent effective N similar to N=4 SYM.

Contribution

It introduces a method to compute anomalous dimensions in cascading theories via minimal surfaces and rotating strings, extending techniques from N=4 SYM to more complex backgrounds.

Findings

Anomalous dimensions resemble N=4 SYM but with a scale-dependent N

Agreement between minimal surface and rotating string calculations

Effective N varies with energy scale in the cascading theory

Abstract

We use light-like Wilson loops and the AdS/CFT correspondence to compute the anomalous dimensions of twist two operators in the cascading (Klebanov-Strassler) theory. The computation amounts to find a minimal surface in the UV region of the KS background which is described by the Klebanov-Tseytlin solution. The result is similar to the one for SU(N), N=4 SYM but with N replaced by an effective, scale dependent N. We perform also a calculation using a rotating string and find agreement. In fact we use a double Wick rotated version of the rotating string solution which is an Euclidean world-sheet ending on a light-like line in the boundary. It gives the same result as the rotating string for the N=4 case but is more appropiate than the rotating string in the N=1 case.