8 research outputs found
Nonmeromorphic operator product expansion and C_2-cofiniteness for a family of W-algebras
We prove the existence and associativity of the nonmeromorphic operator
product expansion for an infinite family of vertex operator algebras, the
triplet W-algebras, using results from P(z)-tensor product theory. While doing
this, we also show that all these vertex operator algebras are C_2-cofinite.Comment: 21 pages, to appear in J. Phys. A: Math. Gen.; the exposition is
improved and one reference is adde
W-extended Kac representations and integrable boundary conditions in the logarithmic minimal models WLM(1,p)
We construct new Yang-Baxter integrable boundary conditions in the lattice
approach to the logarithmic minimal model WLM(1,p) giving rise to reducible yet
indecomposable representations of rank 1 in the continuum scaling limit. We
interpret these W-extended Kac representations as finitely-generated W-extended
Feigin-Fuchs modules over the triplet W-algebra W(p). The W-extended fusion
rules of these representations are inferred from the recently conjectured
Virasoro fusion rules of the Kac representations in the underlying logarithmic
minimal model LM(1,p). We also introduce the modules contragredient to the
W-extended Kac modules and work out the correspondingly-extended fusion
algebra. Our results are in accordance with the Kazhdan-Lusztig dual of tensor
products of modules over the restricted quantum universal enveloping algebra
at . Finally, polynomial fusion rings
isomorphic with the various fusion algebras are determined, and the
corresponding Grothendieck ring of characters is identified.Comment: 28 page
Fusion rules and boundary conditions in the c=0 triplet model
The logarithmic triplet model W_2,3 at c=0 is studied. In particular, we
determine the fusion rules of the irreducible representations from first
principles, and show that there exists a finite set of representations,
including all irreducible representations, that closes under fusion. With the
help of these results we then investigate the possible boundary conditions of
the W_2,3 theory. Unlike the familiar Cardy case where there is a consistent
boundary condition for every representation of the chiral algebra, we find that
for W_2,3 only a subset of representations gives rise to consistent boundary
conditions. These then have boundary spectra with non-degenerate two-point
correlators.Comment: 50 pages; v2: changed formulation in section 1.2.1 and corrected
typos, version to appear in J. Phys.
From boundary to bulk in logarithmic CFT
The analogue of the charge-conjugation modular invariant for rational
logarithmic conformal field theories is constructed. This is done by
reconstructing the bulk spectrum from a simple boundary condition (the analogue
of the Cardy `identity brane'). We apply the general method to the c_1,p
triplet models and reproduce the previously known bulk theory for p=2 at c=-2.
For general p we verify that the resulting partition functions are modular
invariant. We also construct the complete set of 2p boundary states, and
confirm that the identity brane from which we started indeed exists. As a
by-product we obtain a logarithmic version of the Verlinde formula for the
c_1,p triplet models.Comment: 35 pages, 2 figures; v2: minor corrections, version to appear in
J.Phys.