82,937 research outputs found
Algebraic Conformal Field Theories II
Some mathematical questions relating to Coset Conformal Field Theories (CFT)
are considered in the framework of Algebraic Quantum Field Theory as developed
previously by us. We consider the issue of fixed point resolution in the
diagonal coset of type A, and show how to decompose reducible representations
into irreducibles. We show the corresponding coset CFT gives rise to a unitary
tensor modular category in the sense of Turaev, and therefore may be used to
construct 3-manifold invariants. We also show that Kac-Wakimoto Hypothesis
(KWH) and Kac-Wakimoto Conjecture (KWC) are equivalent under general conditions
which can be checked in examples, a result which seems to be hard to prove by
purely representation considerations. Examples are also presented.Comment: 24 pages, AMSte
Recent progress in applying lattice QCD to kaon physics
Standard lattice calculations in kaon physics are based on the evaluation of
matrix elements of local operators between two single-hadron states or a
single-hadron state and the vacuum. Recent progress in lattice QCD has gone
beyond these standard observables. I will review the status and prospects of
lattice kaon physics with an emphasis on non-leptonic decay and
long-distance processes including - mixing and rare kaon
decays.Comment: 23 pages, 13 figures, 3 tables; Plenary talk given at Lattice 201
Algebraic Coset Conformal field theories
All unitary Rational Conformal Field Theories (RCFT) are conjectured to be
related to unitary coset Conformal Field Theories, i.e., gauged
Wess-Zumino-Witten (WZW) models with compact gauge groups. In this paper we use
subfactor theory and ideas of algebraic quantum field theory to approach coset
Conformal Field Theories. Two conjectures are formulated and their consequences
are discussed. Some results are presented which prove the conjectures in
special cases. In particular, one of the results states that a class of
representations of coset () algebras with critical parameters
are irreducible, and under the natural compositions (Connes' fusion), they
generate a finite dimensional fusion ring whose structure constants are
completely determined, thus proving a long-standing conjecture about the
representations of these algebras.Comment: 49 pages, Improved presentations and added details, to appear in
Comm.Math.Phy
On the equivalence of certain coset conformal field theories
We demonstrate the equivalence of Kazama-Suzuki cosets and
based on complex Grassmannians by proving that the corresponding
conformal precosheaves are isomorphic. We also determine all the irreducible
representations of the conformal precosheaves.Comment: 28 pages, Amste
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