73 research outputs found
Contact structures on M × S2 {Mathematical expression}
We show that if a manifold {Mathematical expression} admits a contact structure, then so does {Mathematical expression}. Our proof relies on surgery theory, a theorem of Eliashberg on contact surgery and a theorem of Bourgeois showing that if {Mathematical expression} admits a contact structure then so does {Mathematical expression}. © 2013 Springer-Verlag Berlin Heidelberg
Milnor Numbers of Deformations of Semi-Quasi-Homogeneous Plane Curve Singularities
The aim of this paper is to show the possible Milnor numbers of deformations of semi-quasi-homogeneous isolated plane curve singularity f. Assuming that f is irreducible, one can write f=∑qα+pβ ≥ pqcαβ xαyβ where cp0c0q≠0, 2≤p<q and p, q are coprime. We show that as Milnor numbers of deformations of f one can attain all numbers from μ(f) to μ(f)−r(p−r), where q≡r(mod p). Moreover, we provide an algorithm which produces the desired deformations
Structure in 6D and 4D N=1 supergravity theories from F-theory
We explore some aspects of 4D supergravity theories and F-theory vacua that
are parallel to structures in the space of 6D theories. The spectrum and
topological terms in 4D supergravity theories correspond to topological data of
F-theory geometry, just as in six dimensions. In particular, topological
axion-curvature squared couplings appear in 4D theories; these couplings are
characterized by vectors in the dual to the lattice of axion shift symmetries
associated with string charges. These terms are analogous to the Green-Schwarz
terms of 6D supergravity theories, though in 4D the terms are not generally
linked with anomalies. We outline the correspondence between F-theory topology
and data of the corresponding 4D supergravity theories. The correspondence of
geometry with structure in the low-energy action illuminates topological
aspects of heterotic-F-theory duality in 4D as well as in 6D. The existence of
an F-theory realization also places geometrical constraints on the 4D
supergravity theory in the large-volume limit.Comment: 63 page
A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List
Kreuzer and Skarke famously produced the largest known database of Calabi-Yau threefolds by providing a complete construction of all 473,800,776 reflexive polyhedra that exist in four dimensions [1]. These polyhedra describe the singular limits of ambient toric varieties in which Calabi-Yau threefolds can exist as hypersurfaces. In this paper, we review how to extract topological and geometric information about Calabi-Yau threefolds using the toric construction, and we provide, in a companion online database (see http://nuweb1.neu.edu/cydatabase), a detailed inventory of these quantities which are of interest to physicists. Many of the singular ambient spaces described by the Kreuzer-Skarke list can be smoothed out into multiple distinct toric ambient spaces describing different Calabi-Yau threefolds. We provide a list of the different Calabi-Yau threefolds which can be obtained from each polytope, up to current computational limits. We then give the details of a variety of quantities associated to each of these Calabi-Yau such as Chern classes, intersection numbers, and the Kähler and Mori cones, in addition to the Hodge data. This data forms a useful starting point for a number of physical applications of the Kreuzer-Skarke list
Borcherds Algebras and N=4 Topological Amplitudes
The perturbative spectrum of BPS-states in the E_8 x E_8 heterotic string
theory compactified on T^2 is analysed. We show that the space of BPS-states
forms a representation of a certain Borcherds algebra G which we construct
explicitly using an auxiliary conformal field theory. The denominator formula
of an extension G_{ext} \supset G of this algebra is then found to appear in a
certain heterotic one-loop N=4 topological string amplitude. Our construction
thus gives an N=4 realisation of the idea envisioned by Harvey and Moore,
namely that the `algebra of BPS-states' controls the threshold corrections in
the heterotic string.Comment: 39 page
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