Minimal model boundary flows and c=1 CFT

Abstract

We consider perturbations of unitary minimal models by boundary fields. Initially we consider the models in the limit as c -> 1 and find that the relevant boundary fields all have simple interpretations in this limit. This interpretation allows us to conjecture the IR limits of flows in the unitary minimal models generated by the fields \phi_{rr} of `low' weight. We check this conjecture using the truncated conformal space approach. In the process we find evidence for a new series of integrable boundary flows.Comment: (latex2e, 27 pages, 17 figures

The conformal boundary states for SU(2) at level 1

“…Normally one assumes that there is a single bulk field of weight zero (the identity) but for boundary fields there are many situations in which one may want to have a multiplicity of weight zero fields, for example to consider superpositions of branes or to introduce Chan-Paton factors. The two sets of chiral blocks are related by the so-called fusing matrices (explicit expressions for the fusing matrices of degenerate Virasoro representations at c = 1 relevant here are given in [8]) …”

“…[8] for some examples). We shall now restrict attention to such fundamental boundary conditions α and denote the unique boundary field of weight 0 by 1 1 α .…”

Boundary flows for minimal models

“…This is in agreement with the picture in figure 5, where we have It is also evident from the graph that there are numerous line crossings, which are usually taken to be an indication of integrability. Since the perturbing field in this case φ (33) ≡ φ (12) , this is presumably related in some manner to the a (2) 2 boundary affine Toda theory, in the same manner that φ (1,3) perturbations are related to the boundary sine-Gordon theory.…”

A common limit of super Liouville theory and minimal models

“…Later in [6], Schomerus considered a continuation of Liouville theory to central charge c = 1, and found that it agrees with the Runkel-Watts theory. In [5], the authors also constructed boundary states for this theory as a limit of minimal model boundary states (see also [7]). It was then understood in [8] that these boundary states can be obtained from the ZZ boundary states [9] in Liouville theory.…”

“…For bosonic minimal models, both options have been investigated leading to one discrete family of boundary conditions [7,5], and to one continuous family [8]. For the supersymmetric minimal models we shall only consider the case when the boundary labels are taken to be fixed.…”