2,366 research outputs found
Modular invariance for conformal full field algebras
Let V^L and V^R be simple vertex operator algebras satisfying certain natural
uniqueness-of-vacuum, complete reducibility and cofiniteness conditions and let
F be a conformal full field algebra over the tensor product of V^L and V^R. We
prove that the q_\tau-\bar{q_\tau}-traces (natural traces involving
q_\tau=e^{2\pi i\tau} and \bar{q_\tau}=\bar{e^{2\pi i\tau}}) of geometrically
modified genus-zero correlation functions for F are convergent in suitable
regions and can be extended to doubly periodic functions with periods 1 and
\tau. We obtain necessary and sufficient conditions for these functions to be
modular invariant. In the case that V^L=V^R and F is one of those constructed
by the authors in \cite{HK}, we prove that all these functions are modular
invariant.Comment: 54 page
Full field algebras
We solve the problem of constructing a genus-zero full conformal field theory
(a conformal field theory on genus-zero Riemann surfaces containing both chiral
and antichiral parts) from representations of a simple vertex operator algebra
satisfying certain natural finiteness and reductive conditions. We introduce a
notion of full field algebra which is essentially an algebraic formulation of
the notion of genus-zero full conformal field theory. For two vertex operator
algebras, their tensor product is naturally a full field algebra and we
introduce a notion of full field algebra over such a tensor product. We study
the structure of full field algebras over such a tensor product using modules
and intertwining operators for the two vertex operator algebras. For a simple
vertex operator algebra V satisfying certain natural finiteness and reductive
conditions needed for the Verlinde conjecture to hold, we construct a bilinear
form on the space of intertwining operators for V and prove the nondegeneracy
and other basic properties of this form. The proof of the nondegenracy of the
bilinear form depends not only on the theory of intertwining operator algebras
but also on the modular invariance for intertwining operator algebras through
the use of the results obtained in the proof of the Verlinde conjecture by the
first author. Using this nondegenerate bilinear form, we construct a full field
algebra over the tensor product of two copies of V and an invariant bilinear
form on this algebra.Comment: 66 pages. One reference is added, a minor mistake on the invariance
under \sigma_{23} of the bilinear form on the space of intertwining operators
is corrected and some misprints are fixe
Strong and Electromagnetic Decays of The -wave Heavy Mesons
We calculate the , , , and coupling constants
between the heavy meson doublets and (0^-,1^-)/(0^+,1^+) within the
framework of the light-cone QCD sum rule at the leading order of heavy quark
effective theory. Most of the sum rules are stable with the variations of the
Borel parameter and the continuum threshold. Then we calculate the strong and
electromagnetic decay widths of the D-wave heavy mesons. Their
total widths are around several tens of MeV, which is helpful in the future
experimental search.Comment: 20 pages, 13 figure
Open-string vertex algebras, tensor categories and operads
We introduce notions of open-string vertex algebra, conformal open-string
vertex algebra and variants of these notions. These are
``open-string-theoretic,'' ``noncommutative'' generalizations of the notions of
vertex algebra and of conformal vertex algebra. Given an open-string vertex
algebra, we show that there exists a vertex algebra, which we call the
``meromorphic center,'' inside the original algebra such that the original
algebra yields a module and also an intertwining operator for the meromorphic
center. This result gives us a general method for constructing open-string
vertex algebras. Besides obvious examples obtained from associative algebras
and vertex (super)algebras, we give a nontrivial example constructed from the
minimal model of central charge c=1/2. We establish an equivalence between the
associative algebras in the braided tensor category of modules for a suitable
vertex operator algebra and the grading-restricted conformal open-string vertex
algebras containing a vertex operator algebra isomorphic to the given vertex
operator algebra. We also give a geometric and operadic formulation of the
notion of grading-restricted conformal open-string vertex algebra, we prove two
isomorphism theorems, and in particular, we show that such an algebra gives a
projective algebra over what we call the ``Swiss-cheese partial operad.''Comment: 53 page
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