77 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
Simple currents versus orbifolds with discrete torsion -- a complete classification
We give a complete classification of all simple current modular invariants,
extending previous results for (\Zbf_p)^k to arbitrary centers. We obtain a
simple explicit formula for the most general case. Using orbifold techniques to
this end, we find a one-to-one correspondence between simple current invariants
and subgroups of the center with discrete torsions. As a by-product, we prove
the conjectured monodromy independence of the total number of such invariants.
The orbifold approach works in a straightforward way for symmetries of odd
order, but some modifications are required to deal with symmetries of even
order. With these modifications the orbifold construction with discrete torsion
is complete within the class of simple current invariants. Surprisingly, there
are cases where discrete torsion is a necessity rather than a possibility.Comment: 28 page
Charge sum rules in N=2 theories
Some errors in section 4 are corrected. No change in the results.Comment: 25 page
Klein Bottles and Simple Currents
The standard Klein bottle coefficient in the construction of open descendants
is shown to equal the Frobenius-Schur indicator of a conformal field theory.
Other consistent Klein bottle projections are shown to correspond to simple
currents. These observations enable us to generalize the standard open string
construction from C-diagonal parent theories to include non-standard Klein
bottles. Using (generalizations of) the Frobenius-Schur indicator we prove
positivity and integrality of the resulting open and closed string state
multiplicities for standard as well as non-standard Klein bottles.Comment: 11 pages, LaTeX. References added, minor error correcte
On the classification of (2,1) heterotic strings
We classify all untwisted (2,1) heterotic strings. The only solutions are the
three already known cases, having massless spectra consisting either of 24
chiral fermions, or of 24 bosons, or of 8 scalars and 8 fermions of each
chirality.Comment: Phyzzx and Tables macro packages require
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
Open Descendants of Non-Diagonal Invariants
The open descendants of simple current automorphism invariants are
constructed. We consider the case where the order of the current is two or odd.
We prove that our solutions satisfy the completeness conditions, positivity and
integrality of the open and closed sectors and the Klein bottle constraint
(apart from an interesting exception). In order to do this, we derive some new
relations between the tensor Y and the fixed point conformal field theory. Some
non-standard Klein bottle projections are considered as well.Comment: 21 pages, LaTe
Fixed point resolution in extended WZW-models
A formula is derived for the fixed point resolution matrices of simple
current extended WZW-models and coset conformal field theories. Unlike the
analogous matrices for unextended WZW-models, these matrices are in general not
symmetric, and they may have field-dependent twists. They thus provide
non-trivial realizations of the general conditions presented in earlier work
with Fuchs and Schweigert.Comment: 21 pages, Phyzz
Simple Current Actions of Cyclic Groups
Permutation actions of simple currents on the primaries of a Rational
Conformal Field Theory are considered in the framework of admissible weighted
permutation actions. The solution of admissibility conditions is presented for
cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the
quadratic group. As a consequence, the primaries of a RCFT with an order n
integral or half-integral spin simple current may be arranged into multiplets
of length k^2 (where k is a divisor of n) or 3k^2 if the spin of the simple
current is half-integral and k is odd.Comment: Added reference, minor change
Asymmetric Gepner Models II. Heterotic Weight Lifting
A systematic study of "lifted" Gepner models is presented. Lifted Gepner
models are obtained from standard Gepner models by replacing one of the N=2
building blocks and the factor by a modular isomorphic model on the
bosonic side of the heterotic string. The main result is that after this change
three family models occur abundantly, in sharp contrast to ordinary Gepner
models. In particular, more than 250 new and unrelated moduli spaces of three
family models are identified. We discuss the occurrence of fractionally charged
particles in these spectra.Comment: 46 pages, 17 figure
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