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T-duality
T-duality (short for target-space duality) in theoretical physics is an equivalence of two physical theories, which may be either quantum field theories or string theories. In the simplest example of this relationship, one of the theories describes strings propagating in a spacetime shaped like a circle of some radius R, while the other theory describes strings propagating on a spacetime shaped like a circle of radius proportional to 1/R. The idea of T-duality was first noted by Bala Sathiapalan in an obscure paper in 1987. The two T-dual theories are equivalent in the sense that all observable quantities in one description are identified with quantities in the dual description. For example, momentum in one description takes discrete values and is equal to the number of times the string winds around the circle in the dual description. The idea of T-duality can be extended to more complicated theories, including superstring theories. The existence of these dualities implies tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Theory
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string acts like a particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity. String theory is a broad and varied subject that attempts to address a number of deep questions of fundamental physics. String theory has contributed a number of advances to mathematical physics, which have been applied to a variety of problems in black hole physics, early universe cosmology, nuclear physics, and condensed matter ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
M-theory
In physics, M-theory is a theory that unifies all Consistency, 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 (physics), field theory called eleven-dimensional supergravity. Although a complete formulation o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mirror Symmetry (string Theory)
In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometry, geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory. Early cases of mirror symmetry were discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String Duality
String duality is a class of symmetries in physics that link different string theories, theories which assume that the fundamental building blocks of the universe are strings instead of point particles. Overview Before the so-called "duality revolution" there were believed to be five distinct versions of string theory, plus the (unstable) bosonic and gluonic theories. Note that in the type IIA and type IIB string theories closed strings are allowed to move everywhere throughout the ten-dimensional space-time (called the ''bulk''), while open strings have their ends attached to D-branes, which are membranes of lower dimensionality (their dimension is odd - 1,3,5,7 or 9 - in type IIA and even - 0,2,4,6 or 8 - in type IIB, including the time direction). Before the 1990s, string theorists believed there were five distinct superstring theories: type I, types IIA and IIB, and the two heterotic string theories ( SO(32) and ''E''8×''E''8). The thinking was that out of these fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
U-duality
In physics, U-duality (short for unified duality)S. Mizoguchi,On discrete U-duality in M-theory, 2000. is a symmetry of string theory or M-theory combining S-duality and T-duality transformations. The term is most often met in the context of the "U-duality (symmetry) group" of M-theory as defined on a particular background space (topological manifold In topology, a topological manifold is a topological space that locally resembles real ''n''- dimensional Euclidean space. Topological manifolds are an important class of topological spaces, with applications throughout mathematics. All manifolds ...). This is the union of all the S-duality and T-duality available in that topology. The narrow meaning of the word "U-duality" is one of those dualities that can be classified neither as an S-duality, nor as a T-duality - a transformation that exchanges a large geometry of one theory with the strong coupling of another theory, for example. References String theory {{string-th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
S-duality
In theoretical physics, S-duality (short for strong–weak duality, or Sen duality) is an equivalence of two physical theories, which may be either quantum field theories or string theories. S-duality is useful for doing calculations in theoretical physics because it relates a theory in which calculations are difficult to a theory in which they are easier. In quantum field theory, S-duality generalizes a well established fact from classical electrodynamics, namely the invariance of Maxwell's equations under the interchange of electric and magnetic fields. One of the earliest known examples of S-duality in quantum field theory is Montonen–Olive duality which relates two versions of a quantum field theory called ''N'' = 4 supersymmetric Yang–Mills theory. Recent work of Anton Kapustin and Edward Witten suggests that Montonen–Olive duality is closely related to a research program in mathematics called the geometric Langlands program. Another realization of S-duality i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SYZ Conjecture
The SYZ conjecture is an attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathematics. The original conjecture was proposed in a paper by Strominger, Yau, and Zaslow, entitled "Mirror Symmetry is ''T''-duality".. Along with the homological mirror symmetry conjecture, it is one of the most explored tools applied to understand mirror symmetry in mathematical terms. While the homological mirror symmetry is based on homological algebra, the SYZ conjecture is a geometrical realization of mirror symmetry. Formulation In string theory, mirror symmetry relates type IIA and type IIB theories. It predicts that the effective field theory of type IIA and type IIB should be the same if the two theories are compactified on mirror pair manifolds. The SYZ conjecture uses this fact to realize mirror symmetry. It starts from considering BPS states of type IIA theories compactified on ''X'', especially 0-branes that have moduli space ''X''. It is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compactification (physics)
In theoretical physics, compactification means changing a theory with respect to one of its Spacetime, 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 function, periodic. Compactification plays an important part in Thermal quantum field theory, thermal field theory where one compactifies time, in string theory where one compactifies the String theory#Extra dimensions, extra dimensions of the theory, and in two- or one-dimensional Solid-state physics, 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 Dimensional reduction, dimensionally reduced. In string theory In string theory, compactification is a generalization of Kaluza–Klein theory.Dean Rickles (2014). '' ... [...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 ( Type I, Type IIA, Type IIB, HO and HE) are regarded as different limits of a single theory tentatively called M-theory. Background One of the deepest open problems in theoretical physics is formulating a theory of quantum gravity. Such a theory incorporates both the theory of general relativity, which describes gravitation and applies to large-scale structures, and quantum mechanics or more specifically quantum field theory, which describes the other three fundamental forces that act on th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compact Dimension
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. In string theory In string theory, compactification is a generalization of Kaluza–Klein theory. Dean Rickles (2014). ''A Brief History of String Theory: From Dual Models to M-Theory.'' Springer, p. 89 n. 44. It tries to reconcile the gap between the c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Andrew Strominger
Andrew Eben Strominger (; born 1955) is an American theoretical physicist who is the director of Harvard's Center for the Fundamental Laws of Nature. He has made significant contributions to quantum gravity and string theory. These include his work on Calabi–Yau compactification and topology change in string theory, and on the stringy origin of black hole entropy. He is a senior fellow at the Society of Fellows, and is the Gwill E. York Professor of Physics. Education Strominger received his bachelor's degree at Harvard College in 1977 and his master's degree at the University of California, Berkeley. He then received his PhD at MIT in 1982 under the supervision of Roman Jackiw. Prior to joining Harvard as a professor in 1997, he held a faculty position at the University of California, Santa Barbara. He is the author of over 200 publications. Research Notable contributions * a paper with Cumrun Vafa that explains the microscopic origin of the black hole entropy, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shing-Tung Yau
Shing-Tung Yau (; ; born April 4, 1949) is a Chinese-American mathematician. He is the director of the Yau Mathematical Sciences Center at Tsinghua University and professor emeritus at Harvard University. Until 2022, Yau was the William Caspar Graustein Professor of Mathematics at Harvard, at which point he moved to Tsinghua. Yau was born in Shantou in 1949, moved to British Hong Kong at a young age, and then moved to the United States in 1969. He was awarded the Fields Medal in 1982, in recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation. Yau is considered one of the major contributors to the development of modern differential geometry and geometric analysis. The impact of Yau's work are also seen in the mathematical and physical fields of convex geometry, algebraic geometry, enumerative geometry, mirror symmetry, general relativity, and string theory, while his work h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
