Completeness of boundary conditions for the critical three-state Potts model

Details Completeness of boundary conditions for the critical three-state Potts model Completeness of boundary conditions for the critical three-state Potts model

1998-06-15

arxiv.org/abs/hep-th/9806121v1

Phys.Lett. B441 (1998) 141-146

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, LaTeX2e

Scientific paper

10.1016/S0370-2693(98)01185-X

We show that the conformally invariant boundary conditions for the three-state Potts model are exhausted by the eight known solutions. Their structure is seen to be similar to the one in a free field theory that leads to the existence of D-branes in string theory. Specifically, the fixed and mixed boundary conditions correspond to Neumann conditions, while the free boundary condition and the new one recently found by Affleck et al [1] have a natural interpretation as Dirichlet conditions for a higher-spin current. The latter two conditions are governed by the Lee\hy Yang fusion rules. These results can be generalized to an infinite series of non-diagonal minimal models, and beyond.

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