The SO(N) principal chiral field on a half-line

TL;DR

This paper studies the integrability of the SO(N) principal chiral model on a half-line, demonstrating classical conserved charges under various boundary conditions and analyzing their quantum persistence, with implications for boundary bound-states.

Contribution

It shows that certain boundary conditions preserve integrability at the quantum level and compares classical results with reflection matrices, providing new insights into boundary effects.

Findings

Classical conserved charges exist for mixed, Dirichlet, and Neumann boundary conditions.

At least one non-trivial boundary condition survives quantization.

Preliminary boundary bound-state predictions based on reflection matrices.

Abstract

We investigate the integrability of the SO(N) principal chiral model on a half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well as pure Dirichlet or Neumann) lead to infinitely many conserved charges classically in involution. We use an anomaly-counting method to show that at least one non-trivial example survives quantization, compare our results with the proposed reflection matrices, and, based on these, make some preliminary remarks about expected boundary bound-states.