16,355 research outputs found
Integrable Lattice Models for Conjugate
A new class of integrable lattice models is presented. These are
interaction-round-a-face models based on fundamental nimrep graphs associated
with the conjugate modular invariants, there being a model for each
value of the rank and level. The Boltzmann weights are parameterized by
elliptic theta functions and satisfy the Yang-Baxter equation for any fixed
value of the elliptic nome q. At q=0, the models provide representations of the
Hecke algebra and are expected to lead in the continuum limit to coset
conformal field theories related to the conjugate modular
invariants.Comment: 18 pages. v2: minor changes, such as page 11 footnot
Spectral Measures for
Spectral measures provide invariants for braided subfactors via fusion
modules. In this paper we study joint spectral measures associated to the
compact connected rank two Lie group and its double cover the compact
connected, simply-connected rank two Lie group , including the McKay
graphs for the irreducible representations of and and their
maximal tori, and fusion modules associated to the modular invariants.Comment: 41 pages, 45 figures. Title changed and notation corrected. arXiv
admin note: substantial text overlap with arXiv:1404.186
Spectral Measures for II: finite subgroups
Joint spectral measures associated to the rank two Lie group , including
the representation graphs for the irreducible representations of and its
maximal torus, nimrep graphs associated to the modular invariants have
been studied. In this paper we study the joint spectral measures for the McKay
graphs (or representation graphs) of finite subgroups of . Using character
theoretic methods we classify all non-conjugate embeddings of each subgroup
into the fundamental representation of and present their McKay graphs,
some of which are new.Comment: 33 pages, 20 figures; minor improvements to exposition. Accepted for
publication in Reviews in Mathematical Physic
Braided Subfactors, Spectral Measures, Planar algebras and Calabi-Yau algebras associated to SU(3) modular invariants
Braided subfactors of von Neumann algebras provide a framework for studying
two dimensional conformal field theories and their modular invariants. We
review this in the context of SU(3) conformal field theories through
corresponding SU(3) braided subfactors and various subfactor invariants
including spectral measures for the nimrep graphs, A_2-planar algebras and
almost Calabi-Yau algebras.Comment: 45 pages, 25 figures. v3: minor correction to Figure 14; v2: figures
of 0-1 parts of graphs included, some minor correction
Spectral Measures for
Spectral measures provide invariants for braided subfactors via fusion
modules. In this paper we study joint spectral measures associated to the rank
two Lie group , including the McKay graphs for the irreducible
representations of and its maximal torus, and fusion modules associated
to all known modular invariants.Comment: 36 pages, 40 figures; correction to Sections 5.4 and 5.5, minor
improvements to expositio
Modular Invariants and Twisted Equivariant K-theory II: Dynkin diagram symmetries
The most basic structure of chiral conformal field theory (CFT) is the
Verlinde ring. Freed-Hopkins-Teleman have expressed the Verlinde ring for the
CFT's associated to loop groups, as twisted equivariant K-theory. We build on
their work to express K-theoretically the structures of full CFT. In
particular, the modular invariant partition functions (which essentially
parametrise the possible full CFTs) have a rich interpretation within von
Neumann algebras (subfactors), which has led to the developments of structures
of full CFT such as the full system (fusion ring of defect lines), nimrep
(cylindrical partition function), alpha-induction etc. Modular categorical
interpretations for these have followed. For the generic families of modular
invariants (i.e. those associated to Dynkin diagram symmetries), we provide a
K-theoretic framework for these other CFT structures, and show how they relate
to D-brane charges and charge-groups. We also study conformal embeddings and
the E7 modular invariant of SU(2), as well as some families of finite group
doubles. This new K-theoretic framework allows us to simplify and extend the
less transparent, more ad hoc descriptions of these structures obtained
previously within CFT.Comment: 49 pages; more explanatory material added; minor correction
Orbifold subfactors from Hecke algebras II --- Quantum doubles and braiding ---
A. Ocneanu has observed that a mysterious orbifold phenomenon occurs in the
system of the M_infinity-M_infinity bimodules of the asymptotic inclusion, a
subfactor analogue of the quantum double, of the Jones subfactor of type
A_2n+1. We show that this is a general phenomenon and identify some of his
orbifolds with the ones in our sense as subfactors given as simultaneous fixed
point algebras by working on the Hecke algebra subfactors of type A of Wenzl.
That is, we work on their asymptotic inclusions and show that the
M_infinity-M_infinity bimodules are described by certain orbifolds (with
ghosts) for SU(3)_3k. We actually compute several examples of the (dual)
principal graphs of the asymptotic inclusions. As a corollary of the
identification of Ocneanu's orbifolds with ours, we show that a non-degenerate
braiding exists on the even vertices of D_2n, n>2.Comment: 37 pages, Late
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