On the large spin limit of twist operators in N=4 SYM

TL;DR

This paper develops a method to analyze the large spin limit of twist operators in N=4 SYM, providing insights into their anomalous dimensions and proposing sum rules for higher-twist states.

Contribution

It introduces a new approach to expand the Baxter equation at large spin for twist 2 and 3 operators, advancing understanding of their anomalous dimensions.

Findings

Large spin expansion of Baxter equation for twist 2 and 3.

Proposed sum rules for singlet states at higher twist.

Enhanced analytical tools for multiloop anomalous dimensions.

Abstract

The long range Bethe Ansatz solution of the mixing problem in N=4 SYM allows to compute in a very efficient way multiloop anomalous dimensions of various composite operators. In the case of sl(2) twist operators it is important to obtain closed expressions for the anomalous dimensions in terms of the Lorentz spin. Conjectures are available altough analytical proofs are missing beyond one-loop. In this paper, we will present a method to expand at large spin the solution of the long range Baxter equation in twist 2 and 3. We will also propose sum rules for special singlet states at higher twist.