Semiclassical Strings in AdS_5 x S^5 and Automorphic Functions

Understand

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.