Exact Correlators in the 't Hooft Limit of the Principal Chiral Model

TL;DR

This paper derives exact form factors for an SU(N) principal chiral model in the large N limit, providing insights into matrix-valued field theories and their applications to higher-dimensional gauge theories.

Contribution

It combines 1/N-expansion with form factor axioms to obtain exact form factors in an integrable SU(N) field theory at large N, a less understood regime.

Findings

Exact form factors for SU(N) principal chiral model derived

Vacuum expectation values of field operators computed

Potential applications to 2+1 dimensional gauge theories

Abstract

The properties of (N X N)-matrix-valued-field theories, in the limit N goes to infinity, are harder to obtain than those for isovector-valued field theories. This is because we know less about the sum of planar diagrams than the sum of bubble/linear diagrams. Combining the 1/N-expansion with the axioms for form factors, exact form factors can be found for the integrable field theory of an SU(N)-valued field in 1+1 dimensions. These form factors can be used to find the vacuum expectation value of the product of two field operators. We briefly mention how the results can be applied to 2+1 dimensional gauge theories.