Abstract |
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[eng] Conformally invariant boundary conditions for minimal models on a cylinder
are classified by pairs of Lie algebras $(A,G)$ of ADE type. For each model, we
consider the action of its (discrete) symmetry group on the boundary
conditions. We find that the invariant ones correspond to the nodes in the
product graph $A \otimes G$ that are fixed by some automorphism. We proceed to
determine the charges of the fields in the various Hilbert spaces, but, in a
general minimal model, many consistent solutions occur. In the unitary models
$(A,A)$, we show that there is a unique solution with the property that the
ground state in each sector of boundary conditions is invariant under the
symmetry group. In contrast, a solution with this property does not exist in
the unitary models of the series $(A,D)$ and $(A,E_6)$. A possible
interpretation of this fact is that a certain (large) number of invariant
boundary conditions have unphysical (negative) classical boundary Boltzmann
weights. We give a tentative characterization of the problematic boundary
conditions.
Comment: 13 pages, REVTeX; reorganized and expanded version; includes a new
section on unitary minimal models; conjectures reformulated, pointing to the
generic existence of negative boundary Boltzmann weights in unitary models |