Instantons on conical half-flat 6-manifolds

We present a general procedure to construct 6-dimensional manifolds with SU(3)-structure from SU(2)-structure 5-manifolds. We thereby obtain half-flat cylinders and sine-cones over 5-manifolds with Sasaki-Einstein SU(2)-structure. They are nearly Kahler in the special case of sine-cones over Sasaki-Einstein 5-manifolds. Both half-flat and nearly Kahler 6-manifolds are prominent in flux compactifications of string theory. Subsequently, we investigate instanton equations for connections on vector bundles over these half-flat manifolds. A suitable ansatz for gauge fields on these 6-manifolds reduces the instanton equation to a set of matrix equations. We finally present some of its solutions and discuss the instanton configurations obtained this way.Comment: 1+32 pages, 1 figure, v2: 6 references added, v2 accepted for publication in JHE

Convex ordering and quantification of quantumness

The characterization of physical systems requires a comprehensive understanding of quantum effects. One aspect is a proper quantification of the strength of such quantum phenomena. Here, a general convex ordering of quantum states will be introduced which is based on the algebraic definition of classical states. This definition resolves the ambiguity of the quantumness quantification using topological distance measures. Classical operations on quantum states will be considered to further generalize the ordering prescription. Our technique can be used for a natural and unambiguous quantification of general quantum properties whose classical reference has a convex structure. We apply this method to typical scenarios in quantum optics and quantum information theory to study measures which are based on the fundamental quantum superposition principle.Comment: 9 pages, 2 figures, revised version; published in special issue "150 years of Margarita and Vladimir Man'ko

Sasakian quiver gauge theories and instantons on cones over lens 5-spaces

We consider SU(3)-equivariant dimensional reduction of Yang-Mills theory over certain cyclic orbifolds of the 5-sphere which are Sasaki-Einstein manifolds. We obtain new quiver gauge theories extending those induced via reduction over the leaf spaces of the characteristic foliation of the Sasaki-Einstein structure, which are projective planes. We describe the Higgs branches of these quiver gauge theories as moduli spaces of spherically symmetric instantons which are SU(3)-equivariant solutions to the Hermitian Yang-Mills equations on the associated Calabi-Yau cones, and further compare them to moduli spaces of translationally-invariant instantons on the cones. We provide an explicit unified construction of these moduli spaces as K\"ahler quotients and show that they have the same cyclic orbifold singularities as the cones over the lens 5-spaces.Comment: v2: 54 pages, accepted for publication in Nuclear Physics

Necessary and sufficient conditions for bipartite entanglement

Necessary and sufficient conditions for bipartite entanglement are derived, which apply to arbitrary Hilbert spaces. Motivated by the concept of witnesses, optimized entanglement inequalities are formulated solely in terms of arbitrary Hermitian operators, which makes them useful for applications in experiments. The needed optimization procedure is based on a separability eigenvalue problem, whose analytical solutions are derived for a special class of projection operators. For general Hermitian operators, a numerical implementation of entanglement tests is proposed. It is also shown how to identify bound entangled states with positive partial transposition.Comment: 7 pages, 2 figur

Gene Flow Between Great Lakes Region Populations of the Canadian Tiger Swallowtail Butterfly, \u3ci\u3ePapilio Canadensis\u3c/i\u3e, Near the Hybrid Zone With \u3ci\u3eP. Glaucus\u3c/i\u3e (Lepidoptera: Papilionidae)

Papilio canadensis were sampled from three locations on either side of Lake Michigan to study gene flow near and through a butterfly hybrid zone. Allele frequencies at four polymorphic enzyme loci, as indicated by allozyme electrophoresis, were similar in all samples. Values for FST were close to zero, indicating that gene flow is high among these populations, even when separated by Lake Michigan. We developed a mitochondrial DNA marker with diagnostic differences between P. canadensis and its parapatric sister species Papilio glaucus, based on PCR-RFLP. P. glaucus haplotypes of this mtDNA marker and P. glaucus alleles of a diagnostic allozyme locus (PGD) were found in P. canadensis populations sampled in Michigan’s Lower Peninsula but not in the Upper Peninsula or Northern Minnesota. The presence of P. glaucus alleles in P. canadensis populations could be due to introgression through hybridization, or could be remnants of a P. glaucus population that was inundated by an influx of P. canadensis alleles

What the Bible is Really About: Decoding the Torah

Professor of Bible, Hebrew Union College-Jewish Institute of Religion, NYC; Author of The Original Torah: The Political Intent of the Bible\u27s Writers.https://digitalcommons.fairfield.edu/bennettcenter-posters/1194/thumbnail.jp

Instantons on sine-cones over Sasakian manifolds

We investigate instantons on sine-cones over Sasaki-Einstein and 3-Sasakian manifolds. It is shown that these conical Einstein manifolds are K"ahler with torsion (KT) manifolds admitting Hermitian connections with totally antisymmetric torsion. Furthermore, a deformation of the metric on the sine-cone over 3-Sasakian manifolds allows one to introduce a hyper-K"ahler with torsion (HKT) structure. In the large-volume limit these KT and HKT spaces become Calabi-Yau and hyper-K"ahler conifolds, respectively. We construct gauge connections on complex vector bundles over conical KT and HKT manifolds which solve the instanton equations for Yang-Mills fields in higher dimensions.Comment: 1+15 pages, 2 figure