Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Worldsheet Form Factors in AdS/CFT

Thomas Klose, Tristan McLoughlin

TL;DR

<3-5 sentence high-level summary>We formulate a bootstrap-like set of form-factor axioms for the massive, integrable, non-relativistic AdS$_5\times$S$^5$ worldsheet theory and verify them perturbatively in the near-plane-wave and near-flat limits. The work then connects these worldsheet form factors to weakly coupled spin-chain observables, showing that the axioms hold on the gauge side and that, at leading order in small momentum, the string results reproduce the spin-chain thermodynamic limit. A non-linear map between worldsheet and spin-chain operators is required for off-shell matching, and the perturbative checks illustrate a consistent interpolation between strong and weak coupling. These results lay groundwork for solving the axioms exactly and for exploring holographic correlations via off-shell string observables.

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.

Worldsheet Form Factors in AdS/CFT

TL;DR

<3-5 sentence high-level summary>We formulate a bootstrap-like set of form-factor axioms for the massive, integrable, non-relativistic AdSS worldsheet theory and verify them perturbatively in the near-plane-wave and near-flat limits. The work then connects these worldsheet form factors to weakly coupled spin-chain observables, showing that the axioms hold on the gauge side and that, at leading order in small momentum, the string results reproduce the spin-chain thermodynamic limit. A non-linear map between worldsheet and spin-chain operators is required for off-shell matching, and the perturbative checks illustrate a consistent interpolation between strong and weak coupling. These results lay groundwork for solving the axioms exactly and for exploring holographic correlations via off-shell string observables.

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.

Paper Structure

This paper contains 29 sections, 113 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Form Factors
  3. Definition of Form Factors
  4. Review of Relativistic Case
  5. String Worldsheet Theory
  6. Form Factor Axioms
  7. Perturbative Computation of Form Factors
  8. Perturbative Computation in Near-Plane-Wave Model
  9. Perturbative Computation in Near-Flat-Space Model
  10. One-field operator
  11. Permutation.
  12. Periodicity.
  13. One-particle pole.
  14. Bound states.
  15. Two-field operator
  16. ...and 14 more sections

Figures (6)

  • Figure 1: Crossing for a Lorentz Invariant S-matrix.
  • Figure 2: Crossing for a Lorentz Invariant S-matrix in terms of rapidity variables.
  • Figure 3: Crossing for a Lorentz Invariant form factor in terms of one rapidity variable.
  • Figure 4: Feynman diagrams for three-particle form factor. There are two more one-loop diagrams which are obtained from this one here by permuting the external legs. Depending on which of the external legs corresponds to the anti-particle, not all of those three diagrams give a non-zero contribution to the form factor.
  • Figure 5: Feynman diagrams for two-particle states.
  • ...and 1 more figures