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

Chains of modular elements and shellability

Let L be a lattice admitting a left-modular chain of length r, not necessarily maximal. We show that if either L is graded or the chain is modular, then the (r-2)-skeleton of L is vertex-decomposable (hence shellable). This proves a conjecture of Hersh. Under certain circumstances, we can find shellings of higher skeleta. For instance, if the left-modular chain consists of every other element of some maximum length chain, then L itself is shellable. We apply these results to give a new characterization of finite solvable groups in terms of the topology of subgroup lattices. Our main tool relaxes the conditions for an EL-labeling, allowing multiple ascending chains as long as they are lexicographically before non-ascending chains. We extend results from the theory of EL-shellable posets to such labelings. The shellability of certain skeleta is one such result. Another is that a poset with such a labeling is homotopy equivalent (by discrete Morse theory) to a cell complex with cells in correspondence to weakly descending chains.Comment: 20 pages, 1 figure; v2 has minor fixes; v3 corrects the technical lemma in Section 4, and improves the exposition throughou

T Duality Between Perturbative Characters of E8⊗E8E_8\otimes E_8 and SO(32) Heterotic Strings Compactified On A Circle

Characters of $E_8\otimes E_8$ and SO(32) heterotic strings involving the full internal symmetry Cartan subalgebra generators are defined after circle compactification so that they are T dual. The novel point, as compared with an earlier study of the type II case (hep-th/9707107), is the appearence of Wilson lines. Using SO(17,1) transformations between the weight lattices reveals the existence of an intermediate theory where T duality transformations are disentangled from the internal symmetry. This intermediate theory corresponds to a sort of twisted compactification of a novel type. Its modular invariance follows from an interesting interplay between three representations of the modular group.Comment: 17 pages LateX 2E, 2 figures (eps

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

T-duality Twists and Asymmetric Orbifolds

We study some aspects of asymmetric orbifolds of tori, with the orbifold group being some $\mathbb{Z}_N$ subgroup of the T-duality group and, in particular, provide a concrete understanding of certain phase factors that may accompany the T-duality operation on the stringy Hilbert space in toroidal compactification. We discuss how these T-duality twist phase factors are related to the symmetry and locality properties of the closed string vertex operator algebra, and clarify the role that they enact in the modular covariance of the orbifold theory, mainly using asymmetric orbifolds of tori which are root lattices as working examples.Comment: 67 pages. v2: references added and typos correcte