Worldsheet dilatation operator for the $AdS$ superstring

TL;DR

This paper introduces a systematic method to compute logarithmic divergences of composite operators in the pure spinor formalism of the AdS5×S5 superstring, facilitating the understanding of operator scaling.

Contribution

It presents a novel systematic approach to derive the dilatation operator for local operators in the pure spinor superstring formalism.

Findings

Computed divergences for key composite operators

Validated the method with known operators

Provided a framework for analyzing operator scaling in AdS/CFT

Abstract

In this work we propose a systematic way to compute the logarithmic divergences of composite operators in the pure spinor description of the $AdS_5\times S^5$ superstring. The computations of these divergences can be summarized in terms of a dilatation operator acting on the local operators. We check our results with some important composite operators of the formalism.