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.October 2005

Quantum sine(h)-Gordon model and classical integrable equations

“…To simplify calculations, it is convenient to trade the variable z to 45) and similarly forw. As is well known, this transformation brings MShG equation (1.5) to the conventional Sinh-Gordon (ShG) equation…”

Baxter's Q-operators for supersymmetric spin chains

“…The first non-trivial densities read [58], 27) where √ n = i √ 2/β is a parameter used in [58] instead of our β in (4.10). Note also that their chiral Bose fields X(u) and Y (u) are related to (4.1) as…”

“…(4.37) with l = 0 appeared in [74]. The full equation with arbitrary values of ℓ and r, in the regime α < −1, was recently considered in [58] in connection with the quantization of the integrable AKNS soliton hierarchy.…”

The integrable structure of nonrational conformal field theory

“…The key observation underlying this calculation is equation (7.6) which relates the reflection amplitude to the asymptotics of the functions q p of KdV theory. These asymptotics were found in [41] based on [23]. To round off the picture, we will now briefly recall how this works.…”

“…These q-functions q p (u) can be characterized as the unique solutions of the functional equations (8.7), (8.8) which have the analytic properties (8.9), the asymptotic behavior (8.11), and the additional property to be non-vanishing within the strip S u . It was shown in [23] that a solution to this set of conditions is given by the Wronskian of certain solutions to the theory -is compared to the one in [49,39], which was based on the conformal symmetry. It would be very interesting further elucidate the interplay between the integrable and the conformal structure of Liouville theory.…”