Philippe Ruelle 1999 J. Phys. A: Math. Gen. 32 8831 doi:10.1088/0305-4470/32/50/305
Symmetric boundary conditions in boundary critical phenomena
Philippe Ruelle
Show affiliationsConformally 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 nodes in the product graph A × 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,E6). A tempting 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.
- PACS
- MSC
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22E60 Lie algebras of Lie groups (For the algebraic theory of Lie algebras, see 17Bxx)
- Subjects
- Dates
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Issue 50 (17 December 1999)
Received 12 July 1999
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Symmetric boundary conditions in boundary critical phenomena
Philippe Ruelle 1999 J. Phys. A: Math. Gen. 32 8831
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