The Experts below are selected from a list of 25758 Experts worldwide ranked by ideXlab platform
Cumrun Vafa - One of the best experts on this subject based on the ideXlab platform.
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kobayashi non hyperbolicity of calabi yau manifolds via Mirror Symmetry
Communications in Mathematical Physics, 2020Co-Authors: Ljudmila Kamenova, Cumrun VafaAbstract:A compact complex manifold is Kobayashi non-hyperbolic if there exists an entire curve on it. Using Mirror Symmetry we establish that there are (possibly singular) elliptic or rational curves on any Calabi–Yau manifold X, whose Mirror dual $${\check{X}}$$ exists and is not “Hodge degenerate”, therefore proving that X is Kobayashi non-hyperbolic. We are not aware of any higher dimensional simply connected Calabi–Yau manifolds that satisfy the “Hodge degenerate” condition.
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geometric engineering Mirror Symmetry and 6d 1 0 4d n 2
arXiv: High Energy Physics - Theory, 2015Co-Authors: Michele Del Zotto, Cumrun Vafa, Dan XieAbstract:We study compactification of 6 dimensional (1,0) theories on T^2. We use geometric engineering of these theories via F-theory and employ Mirror Symmetry technology to solve for the effective 4d N=2 geometry for a large number of the (1,0) theories including those associated with conformal matter. Using this we show that for a given 6d theory we can obtain many inequivalent 4d N=2 SCFTs. Some of these respect the global symmetries of the 6d theory while others exhibit SL(2,Z) duality Symmetry inherited from global diffeomorphisms of the T^2. This construction also explains the 6d origin of moduli space of 4d affine ADE quiver theories as flat ADE connections on T^2. Among the resulting 4d N=2 CFTs we find theories whose vacuum geometry is captured by an LG theory (as opposed to a curve or a local CY geometry). We obtain arbitrary genus curves of class S with punctures from toroidal compactification of (1,0) SCFTs where the curve of the class S theory emerges through Mirror Symmetry. We also show that toroidal compactification of the little string version of these theories can lead to class S theories with no punctures on arbitrary genus Riemann surface.
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dimer models from Mirror Symmetry and quivering amoebae
arXiv: High Energy Physics - Theory, 2005Co-Authors: Bo Feng, Kristian D Kennaway, Cumrun VafaAbstract:Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use Mirror Symmetry to shed light on this: the dimer models live on a T^2 subspace of the T^3 fiber that is involved in Mirror Symmetry and is wrapped by D6-branes. These D6-branes are Mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume.
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Mirror Symmetry
2003Co-Authors: Eric Zaslow, Cumrun Vafa, Ravi Vakil, Kentaro Hori, R P Thomas, Albrecht Klemm, Rahul Pandharipande, Sheldon KatzAbstract:We prove Mirror Symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge Symmetry, with a Landau-Ginzburg theory of Toda type. Standard R -> 1/R duality and dynamical generation of superpotential by vortices are crucial in the derivation. This provides not only a proof of Mirror Symmetry in the case of (local and global) Calabi-Yau manifolds, but also for sigma models on manifolds with positive first Chern class, including deformations of the action by holomorphic isometries.
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disk instantons Mirror Symmetry and the duality web
arXiv: High Energy Physics - Theory, 2001Co-Authors: Mina Aganagic, Albrecht Klemm, Cumrun VafaAbstract:We apply the methods recently developed for computation of type IIA disk instantons using Mirror Symmetry to a large class of D-branes wrapped over Lagrangian cycles of non-compact Calabi-Yau 3-folds. Along the way we clarify the notion of ``flat coordinates'' for the boundary theory. We also discover an integer IR ambiguity needed to define the quantum theory of D-branes wrapped over non-compact Lagrangian submanifolds. In the large $N$ dual Chern-Simons theory, this ambiguity is mapped to the UV choice of the framing of the knot. In a type IIB dual description involving $(p,q)$ 5-branes, disk instantons of type IIA get mapped to $(p,q)$ string instantons. The M-theory lift of these results lead to computation of superpotential terms generated by M2 brane instantons wrapped over 3-cycles of certain manifolds of $G_2$ holonomy.
Jorn Dunkel - One of the best experts on this subject based on the ideXlab platform.
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spontaneous Mirror Symmetry breaking induces inverse energy cascade in 3d active fluids
Proceedings of the National Academy of Sciences of the United States of America, 2017Co-Authors: Jonasz Slomka, Jorn DunkelAbstract:Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain Symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break Mirror Symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls Mirror-Symmetry breaking and the emergence of a 3D inverse cascade.
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spontaneous Mirror Symmetry breaking induces inverse energy cascade in 3d active fluids
arXiv: Fluid Dynamics, 2016Co-Authors: Jonasz Slomka, Jorn DunkelAbstract:Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex-mergers exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain Symmetry breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present direct analytical and numerical evidence for the existence of a robust inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break Mirror-Symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Using large-scale numerical simulations, we further demonstrate how active scale selection controls Mirror-Symmetry breaking and the emergence of a 3D inverse cascade. These results imply that bacteria and other swimming microorganisms can affect fluid and nutrient mixing more strongly than previously thought, and they suggest improved hydrodynamic mixing strategies for microfluidic lab-on-a-chip devices based on active turbulence.
Jonasz Slomka - One of the best experts on this subject based on the ideXlab platform.
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spontaneous Mirror Symmetry breaking induces inverse energy cascade in 3d active fluids
Proceedings of the National Academy of Sciences of the United States of America, 2017Co-Authors: Jonasz Slomka, Jorn DunkelAbstract:Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex growth exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain Symmetry-breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present analytical and numerical evidence for the existence of an inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break Mirror Symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Our simulations further demonstrate how active scale selection controls Mirror-Symmetry breaking and the emergence of a 3D inverse cascade.
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spontaneous Mirror Symmetry breaking induces inverse energy cascade in 3d active fluids
arXiv: Fluid Dynamics, 2016Co-Authors: Jonasz Slomka, Jorn DunkelAbstract:Classical turbulence theory assumes that energy transport in a 3D turbulent flow proceeds through a Richardson cascade whereby larger vortices successively decay into smaller ones. By contrast, an additional inverse cascade characterized by vortex-mergers exists in 2D fluids and gases, with profound implications for meteorological flows and fluid mixing. The possibility of a helicity-driven inverse cascade in 3D fluids had been rejected in the 1970s based on equilibrium-thermodynamic arguments. Recently, however, it was proposed that certain Symmetry breaking processes could potentially trigger a 3D inverse cascade, but no physical system exhibiting this phenomenon has been identified to date. Here, we present direct analytical and numerical evidence for the existence of a robust inverse energy cascade in an experimentally validated 3D active fluid model, describing microbial suspension flows that spontaneously break Mirror-Symmetry. We show analytically that self-organized scale selection, a generic feature of many biological and engineered nonequilibrium fluids, can generate parity-violating Beltrami flows. Using large-scale numerical simulations, we further demonstrate how active scale selection controls Mirror-Symmetry breaking and the emergence of a 3D inverse cascade. These results imply that bacteria and other swimming microorganisms can affect fluid and nutrient mixing more strongly than previously thought, and they suggest improved hydrodynamic mixing strategies for microfluidic lab-on-a-chip devices based on active turbulence.
Hunter L Elliott - One of the best experts on this subject based on the ideXlab platform.
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finding Mirror Symmetry via registration and optimal symmetric pairwise assignment of curves algorithm and results
International Conference on Computer Vision, 2017Co-Authors: Marcelo Cicconet, David G C Hildebrand, Hunter L ElliottAbstract:We demonstrate that the problem of fitting a plane of Mirror Symmetry to data in any Euclidian space can be reduced to the problem of registering two datasets, and that the exactness of the solution depends entirely on the registration accuracy. This new Mirror Symmetry via Registration (MSR) framework involves (1) data reflection with respect to an arbitrary plane, (2) registration of original and reflected datasets, and (3) calculation of the eigenvector of eigenvalue -1 for the transformation matrix representing the reflection and registration mappings. To support MSR, we also introduce a novel 2D registration method based on random sample consensus of an ensemble of normalized cross-correlation matches. We further demonstrate the generality of MSR by testing it on a database of 3D shapes with an iterative closest point registration back-end.
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finding Mirror Symmetry via registration and optimal symmetric pairwise assignment of curves
International Conference on Computer Vision, 2017Co-Authors: Marcelo Cicconet, David G C Hildebrand, Hunter L ElliottAbstract:We demonstrate that the problem of fitting a plane of Mirror Symmetry to data in any Euclidian space can be reduced to the problem of registering two datasets. The exactness of the resulting solution depends entirely on the registration accuracy. This new Mirror Symmetry via Registration (MSR) framework involves (1) data reflection with respect to an arbitrary plane, (2) registration of original and reflected datasets, and (3) calculation of the eigenvector of eigenvalue -1 for the transformation matrix representing the reflection and registration mappings. To support MSR, we also introduce a novel 2D registration method based on random sample consensus of an ensemble of normalized cross-correlation matches. With this as its registration back-end, MSR achieves state-of-the-art performance for Symmetry line detection in two independent 2D testing databases. We further demonstrate the generality of MSR by testing it on a database of 3D shapes with an iterative closest point registration back-end. We finally explore its applicability to examining Symmetry in natural systems by assessing the degree of Symmetry present in myelinated axon reconstructions from a larval zebrafish. Using the MSR-computed plane of Symmetry, we introduce techniques for the optimal symmetric pairwise assignment between axon reconstructions and provide visualizations illustrating how neighborhood relationships between nearby axon pairs compare with the relationships between their Mirror-reflected counterparts along the anteroposterior axis.
Goran Ungar - One of the best experts on this subject based on the ideXlab platform.
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Mirror Symmetry breaking by chirality synchronisation in liquids and liquid crystals of achiral molecules
ChemPhysChem, 2016Co-Authors: Carsten Tschierske, Goran UngarAbstract:Spontaneous Mirror Symmetry breaking is an efficient way to obtain homogeneously chiral agents, pharmaceutical ingredients and materials. It is also in the focus of the discussion around the emergence of uniform chirality in biological systems. Tremendous progress has been made by Symmetry breaking during crystallisation from supercooled melts or supersaturates solutions and by self-assembly on solid surfaces and in other highly ordered structures. However, recent observations of spontaneous Mirror Symmetry breaking in liquids and liquid crystals indicate that it is not limited to the well-ordered solid state. Herein, progress in the understanding of a new dynamic mode of Symmetry breaking, based on chirality synchronisation of transiently chiral molecules in isotropic liquids and in bicontinuous cubic, columnar, smectic and nematic liquid crystalline phases is discussed. This process leads to spontaneous deracemisation in the liquid state under thermodynamic control, giving rise to long-term stable Symmetry-broken fluids, even at high temperatures. These fluids form conglomerates that are capable of extraordinary strong chirality amplification, eventually leading to homochirality and providing a new view on the discussion of emergence of uniform chirality in prebiotic systems.