9,449 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
A method for getting a finite in the IR region from an all-order beta function
The analytical method of QCD running coupling constant is extended to a model
with an all-order beta function which is inspired by the famous
Novikov-Shifman-Vai\-n\-s\-htein-Zakharov beta function of N=1 supersymmetric
gau\-g\-e theories. In the approach presented here, the running coupling is
determined by a transcendental equation with non-elementary integral of the
running scale . In our approach , which reads 0.30642,
does not rely on any dimensional parameters. This is in accordance with results
in the literature on the analytical method of QCD running coupling constant.
The new "analytically im\-p\-roved" running coupling constant is also
compatible with the property of asymptotic freedom.Comment: 5 pages, 3 figure
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