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F-theory
In theoretical physics, F-theory is a branch of string theory developed by Iranian physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi–Yau four-folds. The letter "F" supposedly stands for "Father". Compactifications F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a two-torus. By doing so, one obtains type IIB superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group of large diffeomorphisms of the two-dimensional torus. More generally, one can compactify F-theory on an elliptically fibered manifold ( elliptic fibration), i.e. a fiber bundle whose fiber is a two-dimensional torus (also called an elliptic curve). For example, a subcl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumrun Vafa
Cumrun Vafa ( fa, کامران وفا ; born 1 August 1960) is an Iranian-American theoretical physicist and the Hollis Professor of Mathematics 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 for study at university. He received a Bachelor of Science, B.S. in mathematics and physics from the Massachusetts Institute of Technology (MIT) in 1981. He received his Doctor of Philosophy, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory Landscape
The string theory landscape or landscape of vacua refers to the collection of possible false vacua in string theory,The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See M. Douglas, "The statistics of string / M theory vacua", ''JHEP'' 0305, 46 (2003). ; S. Ashok and M. Douglas, "Counting flux vacua", ''JHEP'' 0401, 060 (2004). together comprising a collective "landscape" of choices of parameters governing compactifications. The term "landscape" comes from the notion of a fitness landscape in evolutionary biology. It was first applied to cosmology by Lee Smolin in his book '' The Life of the Cosmos'' (1997), and was first used in the context of string theory by Leonard Susskind. Compactified Calabi–Yau manifolds In string theory the number of flux vacua is commonly thought to be roughly 10^, but could be 10^ or higher. The large number of possibilities arises from choices of Calabi–Yau manifolds and choices of gen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert Einstein was concerned wit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superstring Theory
Superstring theory is an attempt to explain all of the particles and fundamental forces of nature in one theory by modeling them as vibrations of tiny supersymmetric strings. 'Superstring theory' is a shorthand for supersymmetric string theory because unlike bosonic string theory, it is the version of string theory that accounts for both fermions and bosons and incorporates supersymmetry to model gravity. Since the second superstring revolution, the five superstring theories are regarded as different limits of a single theory tentatively called M-theory. Background The deepest problem in theoretical physics is harmonizing the theory of general relativity, which describes gravitation and applies to large-scale structures (stars, galaxies, super clusters), with quantum mechanics, which describes the other three fundamental forces acting on the atomic scale. The development of a quantum field theory of a force invariably results in infinite possibilities. Physicists developed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiple Time Dimensions
The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy. Similar ideas appear in folklore and fantasy literature. Physics Speculative theories with more than one time dimension have been explored in physics. The additional dimensions may be similar to conventional time, compactified like the additional spatial dimensions in string theory, or components of a complex time (kime). Itzhak Bars has proposed models of a two-time physics, noting in 2001 that "The 2T-physics approach in ''d'' + 2 dimensions offers a highly symmetric and unified version of the phenomena described by 1T-physics in ''d'' dimensions." F-theory describes a 12-dimensional spacetime having two time dimensions, giving it the metric signature (10,2). The existence of a well-posed initial value problem for the ultrahyperbolic equation (a wave equation in more than one time dimension) demonstrates that initial data on a mixed (spacelike a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elliptic Fibration
In mathematics, an elliptic surface is a surface that has an elliptic fibration, in other words a proper morphism with connected fibers to an algebraic curve such that almost all fibers are smooth curves of genus 1. (Over an algebraically closed field such as the complex numbers, these fibers are elliptic curves, perhaps without a chosen origin.) This is equivalent to the generic fiber being a smooth curve of genus one. This follows from proper base change. The surface and the base curve are assumed to be non-singular ( complex manifolds or regular schemes, depending on the context). The fibers that are not elliptic curves are called the singular fibers and were classified by Kunihiko Kodaira. Both elliptic and singular fibers are important in string theory, especially in F-theory. Elliptic surfaces form a large class of surfaces that contains many of the interesting examples of surfaces, and are relatively well understood in the theories of complex manifolds and smooth 4-manifo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string theory conference at the University of Southern California in 1995. Witten's announcement initiated a flurry of research activity known as the second superstring revolution. Prior to Witten's announcement, string theorists had identified five versions of superstring theory. Although these theories initially appeared to be very different, work by many physicists showed that the theories were related in intricate and nontrivial ways. Physicists found that apparently distinct theories could be unified by mathematical transformations called S-duality and T-duality. Witten's conjecture was based in part on the existence of these dualities and in part on the relationship of the string theories to a field theory called eleven-dimensional supergravity. Although a complete formulation of M-theory is not known, such a formu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calabi–Yau Manifold
In algebraic geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Particularly in superstring theory, the extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi–Yau manifold, which led to the idea of mirror symmetry. Their name was coined by , after who first conjectured that such surfaces might exist, and who proved the Calabi conjecture. Calabi–Yau manifolds are complex manifolds that are generalizations of K3 surfaces in any number of complex dimensions (i.e. any even number of real dimensions). They were originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent definitions are sometimes used. Definitions The motivational definition given by Shing-Tung Yau is of a compact Kähl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compactification (physics)
In theoretical physics, compactification means changing a theory with respect to one of its space-time dimensions. Instead of having a theory with this dimension being infinite, one changes the theory so that this dimension has a finite length, and may also be periodic. Compactification plays an important part in thermal field theory where one compactifies time, in string theory where one compactifies the extra dimensions of the theory, and in two- or one-dimensional solid state physics, where one considers a system which is limited in one of the three usual spatial dimensions. At the limit where the size of the compact dimension goes to zero, no fields depend on this extra dimension, and the theory is dimensionally reduced. Compactification in quantum field theory Any two-dimensional scalar quantum field theory with a generic potential presents a universal feature, first unveiled by Campos Delgado and Dogaru, namely it is equivalent to a one-dimensional theory of particles, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axion
An axion () is a hypothetical elementary particle postulated by the Peccei–Quinn theory in 1977 to resolve the strong CP problem in quantum chromodynamics (QCD). If axions exist and have low mass within a specific range, they are of interest as a possible component of cold dark matter. History Strong CP problem As shown by Gerard 't Hooft, strong interactions of the standard model, QCD, possess a non-trivial vacuum structure that in principle permits violation of the combined symmetries of charge conjugation and parity, collectively known as CP. Together with effects generated by weak interactions, the effective periodic strong CP-violating term, , appears as a Standard Model input – its value is not predicted by the theory, but must be measured. However, large CP-violating interactions originating from QCD would induce a large electric dipole moment (EDM) for the neutron. Experimental constraints on the currently unobserved EDM implies CP violation from QCD must be e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dilaton
In particle physics, the hypothetical dilaton particle is a particle of a scalar field \varphi that appears in theories with extra dimensions when the volume of the compactified dimensions varies. It appears as a radion in Kaluza–Klein theory's compactifications of extra dimensions. In Brans–Dicke theory of gravity, Newton's constant is not presumed to be constant but instead 1/''G'' is replaced by a scalar field \varphi and the associated particle is the dilaton. Exposition In Kaluza–Klein theories, after dimensional reduction, the effective Planck mass varies as some power of the volume of compactified space. This is why volume can turn out as a dilaton in the lower-dimensional effective theory. Although string theory naturally incorporates Kaluza–Klein theory that first introduced the dilaton, perturbative string theories such as type I string theory, type II string theory, and heterotic string theory already contain the dilaton in the maximal number of 10 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vacua
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a ''perfect'' vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is considerably lower than atmospheric pressure. The Latin term ''in vacuo'' is used to describe an object that is surrounded by a vacuum. The ''quality'' of a partial vacuum refers to how closely it approaches a perfect vacuum. Other things equal, lower gas pressure means higher-quality vacuum. For example, a typical vacuum cleaner produces enough suction to reduce air pressure by around 20%. But high ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
