Integrable and Conformal Twisted Boundary Conditions for sl(2) A-D-E Lattice Models
نویسندگان
چکیده
We study integrable realizations of conformal twisted boundary conditions for sl(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical G = A,D,E lattice models with positive spectral parameter u > 0 and Coxeter number g. Integrable seams are constructed by fusing blocks of elementary local face weights. The usual A-type fusions are labelled by the Kac labels (r, s) and are associated with the Verlinde fusion algebra. We introduce a new type of fusion in the two braid limits u → ±i∞ associated with the graph fusion algebra, and labelled by nodes a, b ∈ G respectively. When combined with automorphisms, they lead to general integrable seams labelled by x = (r, a, b, κ) ∈ (Ag−2,H,H,Z2) where H is the graph G itself for Type I theories and its parent for Type II theories. Identifying our construction labels with the conformal labels of Petkova and Zuber, we find that the integrable seams are in one-to-one correspondence with the conformal seams. The distinct seams are thus associated with the nodes of the Ocneanu quantum graph. The quantum symmetries and twisted partition functions are checked numerically for |G| ≤ 6. We also show, in the case of D2l, that the noncommutativity of the Ocneanu algebra of seams arises because the automorphisms do not commute with the fusions.
منابع مشابه
Integrable Lattice Realizations of Conformal Twisted Boundary Conditions
We construct integrable lattice realizations of conformal twisted boundary conditions for ŝl(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical A-D-E lattice models with positive spectral parameter. The integrable seam boundary conditions are labelled by (r, s, ζ) ∈ (Ag−2, Ag−1,Γ) where Γ is the group of automorphisms of ...
متن کاملIntegrable Boundaries and Universal TBA Functional Equations
We derive the fusion hierarchy of functional equations for critical A-D-E lattice models related to the sl(2) unitary minimal models, the parafermionic models and the supersymmetric models of conformal field theory and deduce the related TBA functional equations. The derivation uses fusion projectors and applies in the presence of all known integrable boundary conditions on the torus and cylind...
متن کاملIntegrable and Conformal Boundary Conditions for Zk Parafermions on a Cylinder
We study integrable and conformal boundary conditions for ŝl(2) Zk parafermions on a cylinder. These conformal field theories are realized as the continuum scaling limit of critical A-D-E lattice models with negative spectral parameter. The conformal boundary conditions labelled by (a,m) ∈ (G,Z2k) are identified with associated integrable lattice boundary conditions labelled by (r, a) ∈ (Ag−2, ...
متن کاملIntegrable and Conformal Boundary Conditions for ŝl(2) A–D–E Lattice Models and Unitary Minimal Conformal Field Theories
Integrable boundary conditions are studied for critical A–D–E and general graph-based lattice models of statistical mechanics. In particular, using techniques associated with the Temperley-Lieb algebra and fusion, a set of boundary Boltzmann weights which satisfies the boundary Yang-Baxter equation is obtained for each boundary condition. When appropriately specialized, these boundary weights, ...
متن کاملTwisted Boundary Conditions
We explore the N = 1 theories compactified on a circle with twisted boundary conditions. The gauge algebra of these theories are the so-called twisted affine Lie algebra. We propose the exact superpotentials by guessing the sum of all monopole-instanton contributions and also by requiring SL(2, Z) modular properties. The latter is inherited from the N = 4 theory, which will be justified in the ...
متن کامل