Integrable boundaries, conformal boundary conditions and A-D-E fusion rules - INSPIRE

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Integrable boundaries, conformal boundary conditions and A-D-E fusion rules

Jul, 1998

4 pages

Published in:

J.Phys.A 31 (1998) L763-L770

e-Print:

hep-th/9807142 [hep-th]

DOI:

10.1088/0305-4470/31/50/001

Report number:

SACLAY-SPH-T-98-076

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Abstract:

The

sl(2)

minimal theories are labelled by a Lie algebra pair

(A,G)

where

G

is of

A

-

D

-

E

type. For these theories on a cylinder we conjecture a complete set of conformal boundary conditions labelled by the nodes of the tensor product graph

A\otimes G

. The cylinder partition functions are given by fusion rules arising from the graph fusion algebra of

A\otimes G

. We further conjecture that, for each conformal boundary condition, an integrable boundary condition exists as a solution of the boundary Yang-Baxter equation for the associated lattice model. The theory is illustrated using the

(A_4,D_4)

or 3-state Potts model.

Note:

4 pages, REVTeX

field theory: conformal
model: minimal
symmetry: SL(2)
boundary condition
algebra: fusion
Yang-Baxter equation
Potts model

References(17)

Figures(0)

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