Semiclassical Strings in AdS_5 x S^5 and Automorphic Functions

TL;DR

This paper derives differential equations for the anomalous dimensions of certain operators in N=4 SYM using AdS/CFT, revealing modular invariance and recurrence relations linked to automorphic functions.

Contribution

It uncovers a hidden modular invariance in the energy-spin relation of folded spinning strings and connects MVV relations to automorphic functions.

Findings

Asymptotic solutions exhibit Gribov-Lipatov reciprocity.

Identifies modular invariance in the energy-spin relation.

Links MVV relations to recurrence relations of automorphic functions.

Abstract

Using AdS/CFT we derive from the folded spinning string ordinary differential equations for the anomalous dimension of the dual N=4 SYM twist-two operators at strong coupling. We show that for large spin the asymptotic solutions have the Gribov-Lipatov recirocity property. To obtain this result we use a hidden modular invariance of the energy-spin relation of the folded spinning string. Further we identify the Moch-Vermaseren-Vogt (MVV) relations, which were first recognized in plain QCD calculations, as the recurrence relations of the asymptotic series ansatz.