668 research outputs found
Dualities in CHL-Models
We define a very general class of CHL-models associated with any string
theory (bosonic or supersymmetric) compactified on an internal CFT C x T^d. We
take the orbifold by a pair (g,\delta), where g is a (possibly non-geometric)
symmetry of C and \delta is a translation along T^d. We analyze the T-dualities
of these models and show that in general they contain Atkin-Lehner type
symmetries. This generalizes our previous work on N=4 CHL-models based on
heterotic string theory on T^6 or type II on K3 x T^2, as well as the
`monstrous' CHL-models based on a compactification of heterotic string theory
on the Frenkel-Lepowsky-Meurman CFT V^{\natural}.Comment: 18 page
BPS Algebras, Genus Zero, and the Heterotic Monster
In this note, we expand on some technical issues raised in \cite{PPV} by the
authors, as well as providing a friendly introduction to and summary of our
previous work. We construct a set of heterotic string compactifications to 0+1
dimensions intimately related to the Monstrous moonshine module of Frenkel,
Lepowsky, and Meurman (and orbifolds thereof). Using this model, we review our
physical interpretation of the genus zero property of Monstrous moonshine.
Furthermore, we show that the space of (second-quantized) BPS-states forms a
module over the Monstrous Lie algebras ---some of the first and
most prominent examples of Generalized Kac-Moody algebras---constructed by
Borcherds and Carnahan. In particular, we clarify the structure of the module
present in the second-quantized string theory. We also sketch a proof of our
methods in the language of vertex operator algebras, for the interested
mathematician.Comment: 19 pages, 2 figure
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
Fricke S-duality in CHL models
open2siopenPersson, Daniel; Volpato, RobertoPersson, Daniel; Volpato, Robert
Crosscaps in Gepner Models and the Moduli space of T2 Orientifolds
We study T^2 orientifolds and their moduli space in detail. Geometrical
insight into the involutive automorphisms of T^2 allows a straightforward
derivation of the moduli space of orientifolded T^2s. Using c=3 Gepner models,
we compare the explicit worldsheet sigma model of an orientifolded T^2
compactification with the CFT results. In doing so, we derive
half-supersymmetry preserving crosscap coefficients for generic unoriented
Gepner models using simple current techniques to construct the charges and
tensions of Calabi-Yau orientifold planes. For T^2s we are able to identify the
O-plane charge directly as the number of fixed points of the involution; this
number plays an important role throughout our analysis. At several points we
make connections with the mathematical literature on real elliptic curves. We
conclude with a preliminary extension of these results to elliptically fibered
K3s.Comment: LaTeX, 59 pages, 21 figures (uses axodraw
An Uplifting Discussion of T-Duality
It is well known that string theory has a T-duality symmetry relating circle
compactifications of large and small radius. This symmetry plays a foundational
role in string theory. We note here that while T-duality is order two acting on
the moduli space of compactifications, it is order four in its action on the
conformal field theory state space. More generally, involutions in the Weyl
group which act at points of enhanced symmetry have canonical lifts
to order four elements of , a phenomenon first investigated by J. Tits in
the mathematical literature on Lie groups and generalized here to conformal
field theory. This simple fact has a number of interesting consequences. One
consequence is a reevaluation of a mod two condition appearing in asymmetric
orbifold constructions. We also briefly discuss the implications for the idea
that T-duality and its generalizations should be thought of as discrete gauge
symmetries in spacetime.Comment: 47 pages, claims regarding valued cocycles remove
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