Construction and clustering properties of the 2-d non-linear sigma-model form factors: O(3), O(4), large n examples

TL;DR

This paper investigates the clustering properties of multi-particle form factors in two-dimensional integrable O(n) sigma-models, proposing a general conjecture and testing it in specific cases and expansions.

Contribution

It conjectures the form factor clustering behavior for general O(n) models and provides initial tests in large n and specific cases n=3,4.

Findings

Form factor clustering observed in O(3) model.

Conjecture extends clustering property to general O(n) models.

Initial tests support the conjecture in leading orders.

Abstract

Multi-particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the others. This remarkable property, which goes under the name of form factor clustering, was first observed by Smirnov in the O(3) non-linear sigma-model and has subsequently found useful applications in integrable models without internal symmetry structure. In this paper we conjecture the nature of form factor clustering for the general O(n) sigma-model and make some tests in leading orders of the 1/n expansion and for the special cases n=3,4.