Boundary RG Flow Associated with the AKNS Soliton Hierarchy

TL;DR

This paper explores an integrable boundary flow related to the AKNS hierarchy, providing exact overlap formulas and analyzing the flow's fixed point, contributing to the understanding of quantum integrable systems with boundaries.

Contribution

It introduces a novel integrable boundary flow with conserved charges and derives exact overlap expressions in terms of differential equations.

Findings

Boundary flow terminates at a nontrivial infrared fixed point.

Exact overlap amplitudes are expressed via solutions of linear differential equations.

Identifies the boundary state corresponding to the fixed point.

Abstract

We introduce and study an integrable boundary flow possessing an infinite number of conserving charges which can be thought of as quantum counterparts of the Ablowitz, Kaup, Newell and Segur Hamiltonians. We propose an exact expression for overlap amplitudes of the boundary state with all primary states in terms of solutions of certain ordinary linear differential equation. The boundary flow is terminated at a nontrivial infrared fixed point. We identify a form of whole boundary state corresponding to this fixed point.