Summing Planar Diagrams by an Integrable Bootstrap

TL;DR

This paper develops a method combining 1/N-expansion and form-factor axioms to compute correlation functions in a large-N sigma model, providing corrections to free-field approximations.

Contribution

It introduces a novel approach to calculate form factors in the large-N limit of the sigma model using integrable bootstrap techniques.

Findings

Large-N form factors of the sigma model are derived.

Provides corrections to free-field approximations for the Wightman function.

Method combines 1/N-expansion with form-factor axioms.

Abstract

Correlation functions of matrix-valued fields are not generally known for massive renormalized field theories. We find the large-N limit of form factors of the (1+1)-dimensional sigma model with SU(N) X SU(N) symmetry. These form factors give a correction to the free-field approximation for the N=infinity Wightman function. The method is a combination of the 1/N-expansion of the S-matrix and Smirnov's form-factor axioms. We expand the renormalized field in terms of a free massive Bosonic field as N goes to infinity.