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

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.