74,096 research outputs found
The tensor structure on the representation category of the triplet algebra
We study the braided monoidal structure that the fusion product induces on
the abelian category -mod, the category of representations of
the triplet -algebra . The -algebras are a
family of vertex operator algebras that form the simplest known examples of
symmetry algebras of logarithmic conformal field theories. We formalise the
methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch,
that are widely used in the physics literature and illustrate a systematic
approach to calculating fusion products in non-semi-simple representation
categories. We apply these methods to the braided monoidal structure of
-mod, previously constructed by Huang, Lepowsky and Zhang, to
prove that this braided monoidal structure is rigid. The rigidity of
-mod allows us to prove explicit formulae for the fusion product
on the set of all simple and all projective -modules, which were
first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and
Runkel.Comment: 58 pages; edit: added references and revisions according to referee
reports. Version to appear on J. Phys.
Open-closed field algebras
We introduce the notions of open-closed field algebra and open-closed field
algebra over a vertex operator algebra V. In the case that V satisfies certain
finiteness and reductivity conditions, we show that an open-closed field
algebra over V canonically gives an algebra over a \C-extension of the
Swiss-cheese partial operad. We also give a tensor categorical formulation and
categorical constructions of open-closed field algebras over V.Comment: 55 pages, largely revised, an old subsection is deleted, a few
references are adde
Vertex operator algebras, the Verlinde conjecture and modular tensor categories
Let V be a simple vertex operator algebra satisfying the following
conditions: (i) The homogeneous subspaces of V of weights less than 0 are 0,
the homogeneous subspace of V of weight 0 is spanned by the vacuum and V' is
isomorphic to V as a V-module. (ii) Every weak V-module gradable by nonnegative
integers is completely reducible. (iii) V is C_2-cofinite. We announce a proof
of the Verlinde conjecture for V, that is, of the statement that the matrices
formed by the fusion rules among irreducible V-modules are diagonalized by the
matrix given by the action of the modular transformation \tau\mapsto -1/\tau on
the space of characters of irreducible V-modules. We discuss some consequences
of the Verlinde conjecture, including the Verlinde formula for the fusion
rules, a formula for the matrix given by the action of \tau\mapsto -1/\tau and
the symmetry of this matrix. We also announce a proof of the rigidity and
nondegeneracy property of the braided tensor category structure on the category
of V-modules when V satisfies in addition the condition that irreducible
V-modules not equivalent to V has no nonzero elements of weight 0. In
particular, the category of V-modules has a natural structure of modular tensor
category.Comment: 18 pages. To appear in the Proc. Natl. Acad. Sci. US
N K Pi molecular state with I=1 and J(Pi)=3/2-
The structure of the molecule-like state of with spin-parity
and isospin I=1 is studied within the chiral SU(3) quark
model. First we calculate the , , and phase shifts in the
framework of the resonating group method (RGM), and a qualitative agreement
with the experimental data is obtained. Then we perform a rough estimation for
the energy of , and the effect of the mixing to
the configuration is also considered. The
calculated energy is very close to the threshold of the system. A
detailed investigation is worth doing in the further study.Comment: 11 pages, 3 figures; accepted for publication in Phys. Rev.
Resonating group method study of kaon-nucleon elastic scattering in the chiral SU(3) quark model
The chiral SU(3) quark model is extended to include an antiquark in order to
study the kaon-nucleon system. The model input parameters , ,
are taken to be the same as in our previous work which focused on the
nucleon-nucleon and nucleon-hyperon interactions. The mass of the scalar meson
is chosen to be 675 MeV and the mixing of and is
considered. Using this model the kaon-nucleon and partial waves phase
shifts of isospin I=0 and I=1 have been studied by solving a resonating group
method (RGM) equation. The numerical results of , , ,
, and partial waves are in good agreement with the
experimental data while the phase shifts of partial wave are a little
bit too repulsive when the laboratory momentum of the kaon meson is greater
than 500 MeV in this present calculation.Comment: 17 pages, 6 figures. Final version for publicatio
S, P, D, F wave KN phase shifts in the chiral SU(3) quark model
The , , , wave phase shifts have been studied in the chiral
SU(3) quark model by solving a resonating group method equation. The numerical
results of different partial waves are in agreement with the experimental data
except for the cases of and , which are less well described
when the laboratory momentum of the kaon meson is greater than 400 MeV.Comment: Prepared for 10th International Symposium on Meson-Nucleon Physics
and the Structure of the Nucleon (MENU 2004), Beijing, China, 29 Aug - 4 Sep
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