Boundary RG Flow Associated with the AKNS Soliton Hierarchy

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.

arXiv comment54 pages

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• The FZZ-Duality Conjecture - A Proof
• Exact WKB methods in $SU(2)$ $N_f=1$
• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• Non-Linear Integral Equations for the SL(2,R)/U(1) black hole sigma model
• Dirichlet sigma models and mean curvature flow
• Approaching the Self-Dual Point of the Sinh-Gordon model
• The FZZ duality with boundary
• The integrable structure of nonrational conformal field theory
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• Spectral zeta functions of a 1D Schrödinger problem
• A(2|1) spectral equivalences and nonlocal integrals of motion