Author

# 健太郎 矢野

Bio: 健太郎 矢野 is an academic researcher. The author has contributed to research in topics: Differential geometry & Proofs involving covariant derivatives. The author has an hindex of 10, co-authored 11 publications receiving 2384 citations.

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01 Jan 1953

TL;DR: In this paper, the authors proposed a pseudo-harmonic tensors and pseudo-killing tensors in metric Manifolds with Torsion, which can be seen as a kind of semi-simple group spaces.

Abstract: *Frontmatter, pg. i*Preface, pg. v*Contents, pg. vii*Chapter I. Riemannian Manifold, pg. 2*Chapter II. Harmonic and Killing Vectors, pg. 26*Chapter III. Harmonic and Killing Tensors, pg. 59*Chapter IV. Harmonic and Killing Tensors in Flat Manifolds, pg. 77*Chapter V. Deviation from Flatness, pg. 81*Chapter VI. Semi-simple Group Spaces, pg. 90*Chapter VII. Pseudo-harmonic Tensors and Pseudo-Killing Tensors in Metric Manifolds with Torsion, pg. 97*Chapter VIII. Kaehler Manifold, pg. 117*Chapter IX. Supplements, pg. 170*Bibliography, pg. 187*Backmatter, pg. 192

659 citations

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TL;DR: In this paper, two constructions of hyperkahler manifolds, one based on a Legendre transform and one on a sympletic quotient, are described, which can be described geometrically.

Abstract: We describe two constructions of hyperkahler manifolds, one based on a Legendre transform, and one on a sympletic quotient. These constructions arose in the context of supersymmetric nonlinear σ-models, but can be described entirely geometrically. In this general setting, we attempt to clarify the relation between supersymmetry and aspects of modern differential geometry, along the way reviewing many basic and well known ideas in the hope of making them accessible to a new audience.

1,163 citations

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TL;DR: In this paper, the general nonlinear scalar model is studied at asymptotically low temperature near two dimensions, and the low temperature expansion is renormalized and effective algorithms are derived for calculation to all orders in the renormalised expansion.

Abstract: The general nonlinear scalar model is studied at asymptotically low temperature near two dimensions. The low temperature expansion is renormalized and effective algorithms are derived for calculation to all orders in the renormalized expansion. The renormalization group coefficients are calculated in the two loop approximation and topological properties of the renormalization group equations are investigated. Special attention is paid to the infrared instabilities of the fixed points, since they provide the continuum limits of the model.

643 citations

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TL;DR: In this article, the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form ${R}^{1,9\ensuremath{-}d}\ifmmode\times\texttimes\fi{M}_{d},$ were analyzed.

Abstract: We analyze the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form ${R}^{1,9\ensuremath{-}d}\ifmmode\times\else\texttimes\fi{}{M}_{d},$ in the common Neveu-Schwarz--Neveu-Schwarz (NS-NS) sector of type II string theory and also type I or 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. Generalized calibrations naturally appear since the geometries can always arise as solutions describing NS or type I or heterotic fivebranes wrapping calibrated cycles. Some new solutions are presented. In particular we find $d=6$ examples with a fibered structure which preserve $\mathcal{N}=1,2,3$ supersymmetry in type II and include compact type I or heterotic geometries.

491 citations

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TL;DR: In this article, the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory is studied in detail, and semiclassically quantized the closed torodial super-brane on a spacetime (Minkowski)4 × (flat 7-torus) and review some mathematical results that are relevant for path integral quantization.

Abstract: We study in detail the structure of the Lorentz covariant, spacetime supersymmetric 11-dimensional supermembrane theory. We show that for a flat spacetime background, the spacetime supersymmetry becomes an N = 8 world volume (rigid) supersymmetry in a “physical” gauge; we also present the field equations and transformation rules in a “lightcone” gauge. We semiclassically quantize the closed torodial supermembrane on a spacetime (Minkowski)4 × (flat 7-torus), and review some mathematical results that are relevant for path integral quantization.

403 citations