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

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.

61 pages, LaTeX

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• Exact form factors of the O(N) $\sigma$-model
• Summing Planar Diagrams by an Integrable Bootstrap II
• Summing Planar Diagrams by an Integrable Bootstrap
• On the space of quantum fields in massive two-dimensional theories
• Bethe--Salpeter wave functions in integrable models
• Spectrum of local boundary operators from boundary form factor bootstrap
• Single-ion anisotropy in Haldane chains and form factor of the O(3) nonlinear sigma model
• Near-integrability and confinement for high-energy hadron-hadron collisions
• Electron spin resonance shifts in S=1 antiferromagnetic chains
• Asymptotic factorization of n-particle SU(N) form factors