Boundary flows in minimal 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.Comment: 13pgs, harvmac, 2 fig

Fused integrable lattice models with quantum impurities and open boundaries

“…[3]- [7]). There has been also much interest on problems related to quantum impurities, mainly because of the important role they play in low dimensional physics [8], but also because of their relevance to boundary conformal field theory [1,2,9,10]. There are numerous studies related to quantum impurities yielding a great number of interesting and useful results (see e.g.…”

“…[14]- [24], [9,10,25,26,27,29]). In this study in particular the alternating integrable spin chain [34] and the RSOS(q 1 , q 2 ; p) model [35] in the presence of a quantum impurity ("Kondo type" boundaries see e.g.…”

The scaling supersymmetric Yang–Lee model with boundary

“…By means of a "boundary TBA" [13] - [15], ratios of g factors of the boundary CFT can be computed from the bulk and boundary S matrices. (See also [16], [17].) Fractional-spin integrals of motion should be manifested in both the boundary S matrix and the perturbed CFT descriptions [18].…”

Boundary flows for minimal models

“…Finally we should mention that TBA equations for the function g α (L) have been proposed in [17] for the integrable perturbations B (1,r) ± φ (1,3) . So far these have not been subjected to quantitative tests, but they agree with the IR fixed point calculated using perturbation theory (for one direction of the flow) and with TCSA (for the other direction).…”

“…To be explicit, for a generic minimal model this comprises perturbations by fields of type (1, 2), (1,3) and (1,5), and their duals (2, 1), (3, 1) and (5, 1). Further evidence for the integrability of the (1, 3) perturbation on boundary conditions of type B (1,s) is given by the existence of exact TBA equations which are supposed to describe these flows [17]. For the perturbation by φ (1,2) ≡ φ (3,3) the obvious line crossings in figure 9 are usually taken as a clear indication of integrability of the RG flow.…”