Form factors at strong coupling via a Y-system

TL;DR

This paper calculates form factors in planar N=4 Super Yang-Mills at strong coupling using a Y-system derived from minimal surfaces in AdS, linking gauge theory and string theory via integrable systems.

Contribution

It derives a Y-system for form factors at strong coupling in N=4 SYM, connecting minimal surfaces in AdS to integrable TBA equations for a restricted class of operators.

Findings

Y-system functional equations for cross ratios are established.

Form factors are expressed as free energy of a TBA system.

Results apply to operators with small conformal dimension.

Abstract

We compute form factors in planar N=4 Super Yang-Mills at strong coupling. Namely we consider the overlap between an operator insertion and 2n gluons. Through the gauge/string duality these are given by minimal surfaces in AdS space. The surfaces end on an infinite periodic sequence of null segments at the boundary of AdS. We consider surfaces that can be embedded in AdS_3. We derive set of functional equations for the cross ratios as functions of the spectral parameter. These equations are of the form of a Y-system. The integral form of the Y-system has Thermodynamics Bethe Ansatz form. The area is given by the free energy of the TBA system or critical value of Yang-Yang functional. We consider a restricted set of operators which have small conformal dimension.