Embedding nonlinear O(6) sigma model into N=4 super-Yang-Mills theory

TL;DR

This paper demonstrates that the strong coupling limit of the scaling function in planar N=4 SYM theory can be described by the thermodynamic Bethe Ansatz equations of the nonlinear O(6) sigma model, confirming a dual string theory prediction.

Contribution

It shows the integral equation for the scaling function reduces to the TBA equations of the nonlinear O(6) sigma model at strong coupling, linking gauge theory and string theory descriptions.

Findings

The integral equation matches the TBA equations of the O(6) sigma model at strong coupling.

The scaling function aligns with the energy density of the O(6) sigma model in AdS_5xS^5.

Results confirm the duality between gauge theory scaling functions and string theory models.

Abstract

Anomalous dimensions of high-twist Wilson operators have a nontrivial scaling behavior in the limit when their Lorentz spin grows exponentially with the twist. To describe the corresponding scaling function in planar N=4 SYM theory, we analyze an integral equation recently proposed by Freyhult, Rej and Staudacher and argue that at strong coupling it can be casted into a form identical to the thermodynamical Bethe Ansatz equations for the nonlinear O(6) sigma model. This result is in a perfect agreement with the proposal put forward by Alday and Maldacena within the dual string description, that the scaling function should coincide with the energy density of the nonlinear O(6) sigma model embedded into AdS_5xS^5.