Boundary flows in minimal models

TL;DR

This paper explores boundary flows in minimal conformal models using RSOS restrictions and analytic continuation of the boundary sinh-Gordon model, revealing new interpolations between boundary conditions and connections to Kondo models.

Contribution

It introduces a novel approach to describe boundary flows in minimal models via RSOS restrictions and boundary sinh-Gordon analytic continuation, extending the staircase phenomenon.

Findings

Describes boundary flows between conformally invariant boundary conditions.

Shows interpolation between all minimal models and their boundary conditions.

Identifies a boundary roaming trajectory in the c=1 theory related to Kondo models.

Abstract

We discuss in this paper the behaviour of minimal models of conformal theory perturbed by the operator $\Phi_{13}$ at the boundary. Using the RSOS restriction of the sine-Gordon model, adapted to the boundary problem, a series of boundary flows between different set of conformally invariant boundary conditions are described. Generalizing the "staircase" phenomenon discovered by Al. Zamolodchikov, we find that an analytic continuation of the boundary sinh-Gordon model provides a flow interpolation not only between all minimal models in the bulk, but also between their possible conformal boundary conditions. In the particular case where the bulk sinh-Gordon coupling is turned to zero, we obtain a boundary roaming trajectory in the $c=1$ theory that interpolates between all the possible spin $S$ Kondo models.