Comments on World-Sheet Form Factors in AdS/CFT

TL;DR

This paper investigates world-sheet form factors in AdS/CFT, calculating two-particle form factors perturbatively and proposing a method to connect these form factors to finite-volume matrix elements, linking string theory and gauge theory results.

Contribution

It provides the first perturbative calculations of two-particle form factors in the AdS_5 x S^5 string world-sheet theory and introduces a prescription to relate form factors to finite-volume matrix elements.

Findings

Perturbative two-particle form factors match with gauge theory predictions.

The minimal solution reproduces the discontinuities of perturbative calculations.

A new method relates form factors to finite-volume matrix elements in the string world-sheet theory.

Abstract

We study form factors in the light-cone gauge world-sheet theory for strings in AdS_5 x S^5. We perturbatively calculate the two-particle form factor in a closed su(2) sector to one-loop in the near-plane-wave limit and to two-loops in the Maldacena-Swanson limit. We also perturbatively solve the functional equation which follows from the form factor axioms for the world-sheet theory and show that the "minimal" solution correctly reproduces the discontinuities of the perturbative calculations. Finally we propose a prescription, valid for polynomial orders of the inverse world-sheet length, for extracting the finite-volume world-sheet matrix element from the form factors and show that the two-excitation matrix element matches with the thermodynamic limit of the spin-chain description of certain tree-level N=4 SYM structure constants.