2D Principal Chiral Field at Large N as a Possible Solvable 2D String Theory

TL;DR

This paper provides an exact solution for the 2D principal chiral field at infinite N, revealing extended objects in the spectrum and suggesting a possible connection to a solvable 2D string theory.

Contribution

It offers the first explicit solution of the 2D principal chiral model at large N, including ground state energy and spectrum analysis under external fields.

Findings

Ground state energy explicitly calculated for arbitrary external fields.

Inverse logarithmic singularity at the mass gap at large N.

Spectrum contains extended objects rather than point particles.

Abstract

We present the exact and explicit solution of the principal chiral field in two dimensions for an infinitely large rank group manifold. The energy of the ground state is explicitly found for the external Noether's fields of an arbitrary magnitude. At small field we found an inverse logarithmic singularity in the ground state energy at the mass gap which indicates that at $N=\infty$ the spectrum of the theory contains extended objects rather than pointlike particles.