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Ooguri–Vafa Metric
In differential geometry, the Ooguri–Vafa metric is a four-dimensional Hyperkähler metric. The Ooguri–Vafa metric is named after Hirosi Ooguri and Cumrun Vafa, who first described it in 1996 using the Gibbons–Hawking ansatz. Another construction was given by Davide Gaiotto, Gregory Moore and Andrew Neitzke in 2008. Definition The Ooguri–Vafa metric is defined on the four-dimensional total spaces of principal U(1)-bundles over open subsets of the three-dimensional euclidean space \mathbb^3. In particular the whole space results in \mathbb^3\times S^1. Define the elliptical fibers \tau(z)=\frac\log(z) with \tau_1=\operatorname(\tau(z)) and \tau_2=\operatorname(\tau(z)) and let \lambda be the string coupling constant. Further define the scaled spatial coordinate :\mathbf=\left(x,\frac,\frac\right). The metric of Ooguri and Vafa has the form :ds^2=\lambda^2 ^(dt-\mathbf\cdot d\mathbf)^2+V d\mathbf^2/math> where \mathbf=(A_x,A_z,A_) and :A_x=-\tau_1=\frac\log\left(\frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Geometry
Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as classical antiquity, antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Nikolai Lobachevsky, Lobachevsky. The simplest examples of smooth spaces are the Differential geometry of curves, plane and space curves and Differential geometry of surfaces, surfaces in the three-dimensional Euclidean space, and the study of these shapes formed the basis for development of modern differential geometry during the 18th and 19th centuries. Since the late 19th century, differential geometry has grown into a field concerned more generally with geometric structures on differentiable ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hirosi Ooguri
is a theoretical physicist working on quantum field theory, quantum gravity, superstring theory, and their interfaces with mathematics. He is Fred Kavli Professor of Theoretical Physics and Mathematics and the Founding Director of the Walter Burke Institute for Theoretical Physics at California Institute of Technology. He is also the director of the Kavli Institute for the Physics and Mathematics at the University of Tokyo and is the chair of the board of trustees of the Aspen Center for Physics in Colorado. Ooguri aims at discovering mathematical structures in these theories and exploiting them to invent new theoretical tools to solve fundamental questions in physics. In particular, he developed the topological string theory to compute Feynman diagrams in superstring theory and used it to study mysterious quantum mechanical properties of black holes. He also made fundamental contributions to conformal field theories in two dimensions, D-branes in Calabi-Yau manifolds, the AdS/ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumrun Vafa
Cumrun Vafa (, ; born 1 August 1960) is an Iranian-American theoretical physicist and the Hollis Professor of Mathematicks and Natural Philosophy at Harvard University. Early life and education Cumrun Vafa was born in Tehran, Iran on 1 August 1960. He became interested in physics as a young child, specifically how the moon was not falling from the sky, and he later grew his interests in math by high school and was fascinated by how mathematics could predict the movement of objects. He graduated from Alborz High School in Tehran and moved to the United States in 1977 to study at university. He received a B.S. in mathematics and physics from the Massachusetts Institute of Technology (MIT) in 1981. He received his Ph.D. in physics from Princeton University in 1985 after completing a doctoral dissertation, titled "Symmetries, inequalities and index theorems", under the supervision of Edward Witten. Academia After his PhD degree, Vafa became a junior fellow via the Harvard Soc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Species Description
A species description is a formal scientific description of a newly encountered species, typically articulated through a scientific publication. Its purpose is to provide a clear description of a new species of organism and explain how it differs from species that have been previously described or related species. For a species to be considered valid, a species description must follow established guidelines and naming conventions dictated by relevant nomenclature codes. These include the International Code of Zoological Nomenclature (ICZN) for animals, the International Code of Nomenclature for algae, fungi, and plants (ICN) for plants, and the International Committee on Taxonomy of Viruses (ICTV) for viruses. A species description often includes photographs or other illustrations of type material and information regarding where this material is deposited. The publication in which the species is described gives the new species a formal scientific name. Some 1.9 million ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbons–Hawking Ansatz
In mathematics, the Gibbons–Hawking ansatz is a method of constructing gravitational instantons introduced by . It gives examples of hyperkähler manifolds in dimension 4 that are invariant under a circle action. Description Suppose that U is an open subset of \mathbb^3, and let * denote the Hodge star operator on \mathbb^3 with respect to the usual (flat) Euclidean metric. V is a harmonic function defined on U such that the cohomology class \left frac*dV\right/math> is integral, i.e. lies in the image of H^2(U;\mathbb) \hookrightarrow H^2(U;\mathbb). Then there is a U(1)-principal bundle \pi : P \to U equipped with a connection 1-form \eta \in \Omega^1(P;\mathfrak(1)) whose curvature form is d\eta = \pi^*(*dV). Then the Riemannian metric g = V\sum_^ dx_j \otimes dx_j + \frac \eta \otimes \eta is hyperkahler, and typically extends to the boundary of U. Examples Quaternions The usual (flat) metric on the quaternions \mathbb \cong \mathbb^2 is hyperkahler. It can be obtain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Davide Gaiotto
Davide Silvano Achille Gaiotto (born 11 March 1977) is an Italian mathematical physicist who deals with quantum field theories and string theory. He received the Gribov Medal in 2011 and the New Horizons in Physics Prize in 2013. Biography Gaiotto won 1996 the silver medal as Italian participants in the International Mathematical Olympiad and 1995 gold medal at the International Physics Olympiad in Canberra. He was an undergraduate student at Scuola Normale Superiore in Pisa from 1996 to 2000. He then moved to Princeton University, where for his graduate studies he worked under the supervision of Leonardo Rastelli, receiving his PhD in 2004. From 2004 to 2007 he was a post-doctoral researcher at Harvard University, and then from 2007 to 2011 at the Institute for Advanced Study. Since 2011 he has been working at the Perimeter Institute for Theoretical Physics in Waterloo, Ontario. He introduced new techniques in the study and design of four-dimensional (N = 2) supersymmetric con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greg Moore (physicist)
Gregory W. Moore is an American theoretical physicist who specializes in mathematical physics and string theory. Moore is a professor in the Physics and Astronomy Department of Rutgers University and a member of the University's High Energy Theory group. Education Moore received an AB in physics from Princeton University in 1982 and a PhD in the same subject from Harvard University in 1985. Career Moore's research has focused on: D-branes on Calabi–Yau manifolds and BPS state counting; relations to Borcherds products, automorphic forms, black-hole entropy, and wall-crossing; applications of the theory of automorphic forms to conformal field theory, string compactification, black hole entropy counting, and the AdS/CFT correspondence; potential relation between string theory and number theory; effective low energy supergravity theories in string compactification and the computation of nonperturbative stringy effects in effective supergravities; topological field theories, and a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Neitzke
Andrew Neitzke is an American mathematician and theoretical physicist, at Yale University. He works in mathematical physics, mainly in geometric problems arising from physics, particularly from supersymmetric quantum field theory. Education and career Neitzke earned his AB at Princeton University as valedictorian. After one year as a Marshall Scholar for Part III of the Mathematical Tripos at the University of Cambridge, he earned his doctorate in 2005 at Harvard University under the supervision of Cumrun Vafa. After postdoctoral research at the Institute for Advanced Study and Harvard University, he became an assistant professor at the University of Texas at Austin in 2009, and was promoted to full professor by 2019. He moved to Yale University in 2020, at first as associate professor but later in 2020 becoming full professor again. In 2008, he as well as Davide Gaiotto and Gregory Moore gave an alternative construction of the Ooguri–Vafa metric, which was first constructed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coupling Constant
In physics, a coupling constant or gauge coupling parameter (or, more simply, a coupling), is a number that determines the strength of the force exerted in an interaction. Originally, the coupling constant related the force acting between two static bodies to the " charges" of the bodies (i.e. the electric charge for electrostatic and the mass for Newtonian gravity) divided by the distance squared, r^2, between the bodies; thus: G in F=G m_1 m_2/r^2 for Newtonian gravity and k_\text in F=k_\textq_1 q_2/r^2 for electrostatic. This description remains valid in modern physics for linear theories with static bodies and massless force carriers. A modern and more general definition uses the Lagrangian \mathcal (or equivalently the Hamiltonian \mathcal) of a system. Usually, \mathcal (or \mathcal) of a system describing an interaction can be separated into a ''kinetic part'' T and an ''interaction part'' V: \mathcal=T-V (or \mathcal=T+V). In field theory, V always contains 3 fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bessel Function
Bessel functions, named after Friedrich Bessel who was the first to systematically study them in 1824, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary complex number \alpha, which represents the ''order'' of the Bessel function. Although \alpha and -\alpha produce the same differential equation, it is conventional to define different Bessel functions for these two values in such a way that the Bessel functions are mostly smooth functions of \alpha. The most important cases are when \alpha is an integer or half-integer. Bessel functions for integer \alpha are also known as cylinder functions or the cylindrical harmonics because they appear in the solution to Laplace's equation in cylindrical coordinates. Spherical Bessel functions with half-integer \alpha are obtained when solving the Helmholtz equation in spherical coordinates. Applications Bessel's equation arises when finding separa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Physical Review Letters
''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. The journal is considered one of the most prestigious in the field of physics. Over a quarter of Physics Nobel Prize-winning papers between 1995 and 2017 were published in it. ''PRL'' is published both online and as a print journal. Its focus is on short articles ("letters") intended for quick publication. The Lead Editor is Hugues Chaté. The Managing Editor is Robert Garisto. History The journal was created in 1958. Samuel Goudsmit, who was then the editor of '' Physical Review'', the American Physical Society's flagship journal, organized and published ''Letters to the Editor of Physical Review'' into a new standalone journal'','' which became ''Physical Review Letters''. It was the first journal intended for the rapid publication of short articles, a format that eventually became popular in many other fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
