318 research outputs found
Conformal Designs based on Vertex Operator Algebras
We introduce the notion of a conformal design based on a vertex operator
algebra. This notation is a natural analog of the notion of block designs or
spherical designs when the elements of the design are based on self-orthogonal
binary codes or integral lattices, respectively. It is shown that the subspaces
of fixed degree of an extremal self-dual vertex operator algebra form conformal
11-, 7-, or 3-designs, generalizing similar results of Assmus-Mattson and
Venkov for extremal doubly-even codes and extremal even lattices. Other
examples are coming from group actions on vertex operator algebras, the case
studied first by Matsuo. The classification of conformal 6- and 8-designs is
investigated. Again, our results are analogous to similar results for codes and
lattices.Comment: 35 pages with 1 table, LaTe
Some comments on symmetric orbifolds of K3
We consider two dimensional superconformal field theories
in the moduli space of symmetric orbifolds of K3. We complete a classification
of the discrete groups of symmetries of these models, conditional to a series
of assumptions and with certain restrictions. Furthermore, we provide a partial
classification of the set of twining genera, encoding the action of a discrete
symmetry on a space of supersymmetric states in these models. These results
suggest the existence of a number of surprising identities between seemingly
different Borcherds products, representing Siegel modular forms of degree two
and level . We also provide a critical review of various properties of the
moduli space of these superconformal field theories, including the groups of
dualities, the set of singular models and the locus of symmetric orbifold
points, and describe some puzzles related to our (lack of) understanding of
these properties.Comment: 54 pages; v3: various points clarified; appendix E added; matches
with published versio
Fricke S-duality in CHL models
We consider four dimensional CHL models with sixteen spacetime
supersymmetries obtained from orbifolds of type IIA superstring on K3 x T^2 by
a Z_N symmetry acting (possibly) non-geometrically on K3. We show that most of
these models (in particular, for geometric symmetries) are self-dual under a
weak-strong duality acting on the heterotic axio-dilaton modulus S by a "Fricke
involution" S --> -1/NS. This is a novel symmetry of CHL models that lies
outside of the standard SL(2,Z)-symmetry of the parent theory, heterotic
strings on T^6. For self-dual models this implies that the lattice of purely
electric charges is N-modular, i.e. isometric to its dual up to a rescaling of
its quadratic form by N. We verify this prediction by determining the lattices
of electric and magnetic charges in all relevant examples. We also calculate
certain BPS-saturated couplings and verify that they are invariant under the
Fricke S-duality. For CHL models that are not self-dual, the strong coupling
limit is dual to type IIA compactified on T^6/Z_N, for some Z_N-symmetry
preserving half of the spacetime supersymmetries.Comment: 56 pages, 3 figures; v3: some minor mistakes correcte
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