5,650 research outputs found
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
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
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
Continuous Symmetries of Lattice Conformal Field Theories and their -Orbifolds
Following on from a general observation in an earlier paper, we consider the
continuous symmetries of a certain class of conformal field theories
constructed from lattices and their reflection-twisted orbifolds. It is shown
that the naive expectation that the only such (inner) symmetries are generated
by the modes of the vertex operators corresponding to the states of unit
conformal weight obtains, and a criterion for this expectation to hold in
general is proposed.Comment: 15 page
Permutation Orbifold of N=2 Supersymmetric Minimal Models
In this paper we apply the previously derived formalism of permutation
orbifold conformal field theories to N=2 supersymmetric minimal models. By
interchanging extensions and permutations of the factors we find a very
interesting structure relating various conformal field theories that seems not
to be known in literature. Moreover, unexpected exceptional simple currents
arise in the extended permuted models, coming from off-diagonal fields. In a
few situations they admit fixed points that must be resolved. We determine the
complete CFT data with all fixed point resolution matrices for all simple
currents of all Z_2-permutations orbifolds of all minimal N=2 models with k\neq
2 mod 4.Comment: 48 page
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
Permutation orbifolds of heterotic Gepner models
We study orbifolds by permutations of two identical N=2 minimal models within
the Gepner construction of four dimensional heterotic strings. This is done
using the new N=2 supersymmetric permutation orbifold building blocks we have
recently developed. We compare our results with the old method of modding out
the full string partition function. The overlap between these two approaches is
surprisingly small, but whenever a comparison can be made we find complete
agreement. The use of permutation building blocks allows us to use the complete
arsenal of simple current techniques that is available for standard Gepner
models, vastly extending what could previously be done for permutation
orbifolds. In particular, we consider (0,2) models, breaking of SO(10) to
subgroups, weight-lifting for the minimal models and B-L lifting. Some
previously observed phenomena, for example concerning family number
quantization, extend to this new class as well, and in the lifted models three
family models occur with abundance comparable to two or four.Comment: 49 pages, 4 figure
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
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