844 research outputs found
From Dynkin diagram symmetries to fixed point structures
Any automorphism of the Dynkin diagram of a symmetrizable Kac-Moody algebra
induces an automorphism of the algebra and a mapping between its highest weight
modules. For a large class of such Dynkin diagram automorphisms, we can
describe various aspects of these maps in terms of another Kac-Moody algebra,
the `orbit Lie algebra'. In particular, the generating function for the trace
of the map on modules, the `twining character', is equal to a character of the
orbit Lie algebra. Orbit Lie algebras and twining characters constitute a
crucial step towards solving the fixed point resolution problem in conformal
field theory.Comment: Latex, 60 pages (extended version 63 pages), 4 uuencoded figures
Formula (6.25) corrected. While this correction might be important in
applications of our work, the results of the paper are not affected by it. In
the present submission the "extended version" is default. In this version the
corrected formula is (6.32
Quasi-Galois Symmetries of the Modular S-Matrix
The recently introduced Galois symmetries of RCFT are generalized, for the
WZW case, to `quasi-Galois symmetries'. These symmetries can be used to derive
a large number of equalities and sum rules for entries of the modular matrix S,
including some that previously had been observed empirically. In addition,
quasi-Galois symmetries allow to construct modular invariants and to relate
S-matrices as well as modular invariants at different levels. They also lead us
to an extremely plausible conjecture for the branching rules of the conformal
embeddings of g into so(dim g).Comment: 20 pages (A4), LaTe
Twining characters and orbit Lie algebras
We associate to outer automorphisms of generalized Kac-Moody algebras
generalized character-valued indices, the twining characters. A character
formula for twining characters is derived which shows that they coincide with
the ordinary characters of some other generalized Kac-Moody algebra, the
so-called orbit Lie algebra. Some applications to problems in conformal field
theory, algebraic geometry and the theory of sporadic simple groups are
sketched.Comment: 6 pages, LaTeX, Talk given by C. Schweigert at the XXI international
colloquium on group theoretical methods in physics, July 1996, Goslar,
German
A matrix S for all simple current extensions
A formula is presented for the modular transformation matrix S for any simple
current extension of the chiral algebra of a conformal field theory. This
provides in particular an algorithm for resolving arbitrary simple current
fixed points, in such a way that the matrix S we obtain is unitary and
symmetric and furnishes a modular group representation. The formalism works in
principle for any conformal field theory. A crucial ingredient is a set of
matrices S^J_{ab}, where J is a simple current and a and b are fixed points of
J. We expect that these input matrices realize the modular group for the torus
one-point functions of the simple currents. In the case of WZW-models these
matrices can be identified with the S-matrices of the orbit Lie algebras that
we introduced in a previous paper. As a special case of our conjecture we
obtain the modular matrix S for WZW-theories based on group manifolds that are
not simply connected, as well as for most coset models.Comment: Phyzzx, 53 pages 1 uuencoded figure Arrow in figure corrected;
Forgotten acknowledment to funding organization added; DESY preprint-number
adde
Galois Modular Invariants of WZW Models
The set of modular invariants that can be obtained from Galois
transformations is investigated systematically for WZW models. It is shown that
a large subset of Galois modular invariants coincides with simple current
invariants. For algebras of type B and D infinite series of previously unknown
exceptional automorphism invariants are found.Comment: phyzzx macros, 38 pages. NIKHEF-H/94-3
Hanbury Brown Twiss effect for ultracold quantum gases
We have studied 2-body correlations of atoms in an expanding cloud above and
below the Bose-Einstein condensation threshold. The observed correlation
function for a thermal cloud shows a bunching behavior, while the correlation
is flat for a coherent sample. These quantum correlations are the atomic
analogue of the Hanbury Brown Twiss effect. We observe the effect in three
dimensions and study its dependence on cloud size.Comment: Figure 1 availabl
Twisted Open Strings from Closed Strings: The WZW Orientation Orbifolds
Including {\it world-sheet orientation-reversing automorphisms}
in the orbifold program, we construct the operator
algebras and twisted KZ systems of the general WZW {\it orientation orbifold}
. We find that the orientation-orbifold sectors corresponding
to each are {\it twisted open} WZW strings, whose
properties are quite distinct from conventional open-string orientifold
sectors. As simple illustrations, we also discuss the classical (high-level)
limit of our construction and free-boson examples on abelian .Comment: 65 pages, typos correcte
Boundaries, crosscaps and simple currents
Universal formulas for the boundary and crosscap coefficients are presented,
which are valid for all symmetric simple current modifications of the charge
conjugation invariant of any rational conformal field theory.Comment: 11 pages, LaTeX2e, reference added, typos correcte
Automorphism Modular Invariants of Current Algebras
We consider those two-dimensional rational conformal field theories (RCFTs)
whose chiral algebras, when maximally extended, are isomorphic to the current
algebra formed from some affine non-twisted Kac--Moody algebra at fixed level.
In this case the partition function is specified by an automorphism of the
fusion ring and corresponding symmetry of the Kac--Peterson modular matrices.
We classify all such partition functions when the underlying finite-dimensional
Lie algebra is simple. This gives all possible spectra for this class of RCFTs.
While accomplishing this, we also find the primary fields with second smallest
quantum dimension.Comment: 32 pages, plain Te
Comments on the classification of orientifolds
The simple current construction of orientifolds based on rational conformal
field theories is reviewed. When applied to SO(16) level 1, one can describe
all ten-dimensional orientifolds in a unified framework.Comment: 9 pages, Contribution to proceedings of RTN-workshop in Leuven,
Belgium, September 200
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