Worldsheet Form Factors in AdS/CFT

TL;DR

This paper develops and verifies consistency conditions for worldsheet form factors in the integrable, non-relativistic AdS(5) x S**5 string theory, connecting string theory and spin-chain models.

Contribution

It formulates new consistency conditions for worldsheet form factors in AdS/CFT and verifies them at tree and one-loop levels, bridging string theory and spin-chain descriptions.

Findings

Conditions hold at tree level in near-plane-wave limit.

Conditions verified at one loop in near-flat limit.

Form factors match spin-chain thermodynamic limit at leading order.

Abstract

We formulate a set of consistency conditions appropriate to worldsheet form factors in the massive, integrable but non-relativistic, light-cone gauge fixed AdS(5) x S**5 string theory. We then perturbatively verify that these conditions hold, at tree level in the near-plane-wave limit and to one loop in the near-flat (Maldacena-Swanson) limit, for a number of specific cases. We further study the form factors in the weakly coupled dual description, verifying that the relevant conditions naturally hold for the one-loop Heisenberg spin-chain. Finally, we note that the near-plane-wave expressions for the form factors, when further expanded in small momentum or, equivalently, large charge density, reproduce the thermodynamic limit of the spin-chain results at leading order.