171 research outputs found
Classification of Supersymmetric Flux Vacua in M Theory
We present a comprehensive classification of supersymmetric vacua of M-theory
compactification on seven-dimensional manifolds with general four-form fluxes.
We analyze the cases where the resulting four-dimensional vacua have N =
1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2
structures. In particular, we find for N = 2 supersymmetry, that the external
space-time is Minkowski and the base manifold of the internal space is
conformally K\"ahler for SU(2) structures, while for SU(3) structures the
internal space has to be Einstein-Sasaki and no internal fluxes are allowed.
Moreover, we provide a new vacuum with N = 1 supersymmetry and SU(3) structure,
where all fluxes are non-zero and the first order differential equations are
solved.Comment: 50 pages, clarification of the spinor ansatz added, references added,
typos correcte
Highly Unsaturated Binuclear Butadiene Iron Carbonyls: Quintet Spin States, Perpendicular Structures, Agostic Hydrogen Atoms, and Iron-Iron Multiple Bonds
The highly unsaturated binuclear butadiene iron carbonyls (C4H6)2Fe2(CO)n (n = 2, 1) have been examined using density functional theory. For (C4H6)2Fe2(CO)n (n = 2, 1), both coaxial and perpendicular structures are found. The global minima of (C4H6)2Fe2(CO)n (n = 2, 1) are the perpendicular structures 2Q-1 and 1Q-1, respectively, with 17- and 15-electron configurations for the iron atoms leading to quintet spin states. The Fe=Fe distance of 2.361 Ă
(M06-L) in the (C4H6)2Fe2(CO)2 structure 2Q-1 suggests a formal double bond. The FeâĄFe bond distance in the (C4H6)2Fe2(CO) structure 1Q-1 is even shorter at 2.273 Ă
(M06-L), suggesting a triple bond. Higher energy (C4H6)2Fe2(CO)n (n = 2, 1) structures include structures in which a bridging butadiene ligand is bonded to one of the iron atoms as a tetrahapto ligand and to the other iron atom through two agostic hydrogen atoms from the end CH2 groups. Singlet (C4H6)2Fe2(CO) structures with formal FeâFe quadruple bonds of lengths âŒ2.05 Ă
were also found but at very high energies (âŒ47 kcal/mol) relative to the global minimum
Pairing-based algorithms for jacobians of genus 2 curves with maximal endomorphism ring
Using Galois cohomology, Schmoyer characterizes cryptographic non-trivial
self-pairings of the -Tate pairing in terms of the action of the
Frobenius on the -torsion of the Jacobian of a genus 2 curve. We apply
similar techniques to study the non-degeneracy of the -Tate pairing
restrained to subgroups of the -torsion which are maximal isotropic with
respect to the Weil pairing. First, we deduce a criterion to verify whether the
jacobian of a genus 2 curve has maximal endomorphism ring. Secondly, we derive
a method to construct horizontal -isogenies starting from a
jacobian with maximal endomorphism ring
New supersymmetric AdS4 type II vacua
Building on our recent results on dynamic SU(3)xSU(3) structures we present a
set of sufficient conditions for supersymmetric AdS4xM6 backgrounds of type
IIA/IIB supergravity. These conditions ensure that the background solves,
besides the supersymmetry equations, all the equations of motion of type II
supergravity. The conditions state that the internal manifold is locally a
codimension-one foliation such that the five dimensional leaves admit a
Sasaki-Einstein structure. In type IIA the supersymmetry is N=2, and the total
six-dimensional internal space is locally an S^2 bundle over a four-dimensional
Kaehler-Einstein base; in IIB the internal space is the direct product of a
circle and a five-dimensional squashed Sasaki-Einstein manifold. Given any
five-dimensional Sasaki-Einstein manifold we construct the corresponding
families of type IIA/IIB vacua. The precise profiles of all the fields are
determined at the solution and depend on whether one is in IIA or in IIB. In
particular the background does not contain any sources, all fluxes (including
the Romans mass in IIA) are generally non-zero, and the dilaton and warp factor
are non-constant.Comment: 19 pages; clarifications added, version to appear in JHE
Superstrings with Intrinsic Torsion
We systematically analyse the necessary and sufficient conditions for the
preservation of supersymmetry for bosonic geometries of the form R^{1,9-d}
\times M_d, in the common NS-NS sector of type II string theory and also type
I/heterotic string theory. The results are phrased in terms of the intrinsic
torsion of G-structures and provide a comprehensive classification of static
supersymmetric backgrounds in these theories. Generalised calibrations
naturally appear since the geometries always admit NS or type I/heterotic
fivebranes wrapping calibrated cycles. Some new solutions are presented. In
particular we find d=6 examples with a fibred structure which preserve N=1,2,3
supersymmetry in type II and include compact type I/heterotic geometries.Comment: 58 pages, LaTeX; v2: New section on solutions including an example
with N=3 supersymmetry and discussion of heterotic compactifications. Details
on conventions and references added. v3: added an explicit example of
non-integrable product structure in Appendix C; some typos fixe
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