Integrable Boundary Conditions and W-Extended Fusion in the Logarithmic Minimal Models LM(1,p)

Abstract

We consider the logarithmic minimal models LM(1,p) as `rational' logarithmic conformal field theories with extended W symmetry. To make contact with the extended picture starting from the lattice, we identify 4p-2 boundary conditions as specific limits of integrable boundary conditions of the underlying Yang-Baxter integrable lattice models. Specifically, we identify 2p integrable boundary conditions to match the 2p known irreducible W-representations. These 2p extended representations naturally decompose into infinite sums of the irreducible Virasoro representations (r,s). A further 2p-2 reducible yet indecomposable W-representations of rank 2 are generated by fusion and these decompose as infinite sums of indecomposable rank-2 Virasoro representations. The fusion rules in the extended picture are deduced from the known fusion rules for the Virasoro representations of LM(1,p) and are found to be in agreement with previous works. The closure of the fusion algebra on a finite number of representations in the extended picture is remarkable confirmation of the consistency of the lattice approach.

15 pages

References in corpus (9)

• From Percolation to Logarithmic Conformal Field Theory
• Virasoro representations and fusion for general augmented minimal models
• From boundary to bulk in logarithmic CFT
• Fusion Algebras of Logarithmic Minimal Models
• The logarithmic triplet theory with boundary
• Logarithmic M(2,p) Minimal Models, their Logarithmic Couplings, and Duality
• Radford, Drinfeld, and Cardy boundary states in (1,p) logarithmic conformal field models
• On Verlinde-Like Formulas in c_{p,1} Logarithmic Conformal Field Theories
• Pair correlations in sandpile model: a check of logarithmic conformal field theory

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• Coset Graphs in Bulk and Boundary Logarithmic Minimal Models
• Critical dense polymers with Robin boundary conditions, half-integer Kac labels and ${\mathbb{Z}}_4$ fermions
• Two-dimensional spanning webs as (1,2) logarithmic minimal model
• Hopf algebras and finite tensor categories in conformal field theory
• Characters of coinvariants in (1,p) logarithmic models