1,491 research outputs found
Integrable Lattice Realizations of N=1 Superconformal Boundary Conditions
We construct integrable boundary conditions for sl(2) coset models with
central charges c=3/2-12/(m(m+2)) and m=3,4,... The associated cylinder
partition functions are generating functions for the branching functions but
these boundary conditions manifestly break the superconformal symmetry. We show
that there are additional integrable boundary conditions, satisfying the
boundary Yang-Baxter equation, which respect the superconformal symmetry and
lead to generating functions for the superconformal characters in both Ramond
and Neveu-Schwarz sectors. We also present general formulas for the cylinder
partition functions. This involves an alternative derivation of the
superconformal Verlinde formula recently proposed by Nepomechie.Comment: 22 pages, 12 figures; section 2 rewritten; journal-ref. adde
Fusion hierarchies, -systems and -systems for the dilute loop models
The fusion hierarchy, -system and -system of functional equations are
the key to integrability for 2d lattice models. We derive these equations for
the generic dilute loop models. The fused transfer matrices are
associated with nodes of the infinite dominant integral weight lattice of
. For generic values of the crossing parameter , the -
and -systems do not truncate. For the case
rational so that
is a root of unity, we find explicit closure
relations and derive closed finite - and -systems. The TBA diagrams of
the -systems and associated Thermodynamic Bethe Ansatz (TBA) integral
equations are not of simple Dynkin type. They involve nodes if is
even and nodes if is odd and are related to the TBA diagrams of
models at roots of unity by a folding which originates
from the addition of crossing symmetry. In an appropriate regime, the known
central charges are . Prototypical examples of the
loop models, at roots of unity, include critical dense polymers
with central charge , and loop
fugacity and critical site percolation on the triangular lattice
with , and . Solving
the TBA equations for the conformal data will determine whether these models
lie in the same universality classes as their counterparts. More
specifically, it will confirm the extent to which bond and site percolation lie
in the same universality class as logarithmic conformal field theories.Comment: 34 page
Fusion of \ade Lattice Models
Fusion hierarchies of \ade face models are constructed. The fused critical
, and elliptic models yield new solutions of the Yang-Baxter
equations with bond variables on the edges of faces in addition to the spin
variables on the corners. It is shown directly that the row transfer matrices
of the fused models satisfy special functional equations. Intertwiners between
the fused \ade models are constructed by fusing the cells that intertwine the
elementary face weights. As an example, we calculate explicitly the fused
face weights of the 3-state Potts model associated with the
diagram as well as the fused intertwiner cells for the --
intertwiner. Remarkably, this fusion yields the face weights of
both the Ising model and 3-state CSOS models.Comment: 41 page
Intertwiners and \ade Lattice Models
Intertwiners between \ade lattice models are presented and the general theory
developed. The intertwiners are discussed at three levels: at the level of the
adjacency matrices, at the level of the cell calculus intertwining the face
algebras and at the level of the row transfer matrices. A convenient graphical
representation of the intertwining cells is introduced. The utility of the
intertwining relations in studying the spectra of the \ade models is
emphasized. In particular, it is shown that the existence of an intertwiner
implies that many eigenvalues of the \ade row transfer matrices are exactly in
common for a finite system and, consequently, that the corresponding central
charges and scaling dimensions can be identified.Comment: 48 pages, Two postscript files included
Solutions of the boundary Yang-Baxter equation for ADE models
We present the general diagonal and, in some cases, non-diagonal solutions of
the boundary Yang-Baxter equation for a number of related
interaction-round-a-face models, including the standard and dilute A_L, D_L and
E_{6,7,8} models.Comment: 32 pages. Sections 7.2 and 9.2 revise
Grothendieck ring and Verlinde-like formula for the W-extended logarithmic minimal model WLM(1,p)
We consider the Grothendieck ring of the fusion algebra of the W-extended
logarithmic minimal model WLM(1,p). Informally, this is the fusion ring of
W-irreducible characters so it is blind to the Jordan block structures
associated with reducible yet indecomposable representations. As in the
rational models, the Grothendieck ring is described by a simple graph fusion
algebra. The 2p-dimensional matrices of the regular representation are mutually
commuting but not diagonalizable. They are brought simultaneously to Jordan
form by the modular data coming from the full (3p-1)-dimensional S-matrix which
includes transformations of the p-1 pseudo-characters. The spectral
decomposition yields a Verlinde-like formula that is manifestly independent of
the modular parameter but is, in fact, equivalent to the Verlinde-like
formula recently proposed by Gaberdiel and Runkel involving a -dependent
S-matrix.Comment: 13 pages, v2: example, comments and references adde
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