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D-brane
In string theory, D-branes, short for Dirichlet membrane, are a class of extended objects upon which open strings can end with Dirichlet boundary conditions, after which they are named. D-branes are typically classified by their spatial dimension, which is indicated by a number written after the ''D.'' A D0-brane is a single point, a D1-brane is a line (sometimes called a "D-string"), a D2-brane is a plane, and a D25-brane fills the highest-dimensional space considered in bosonic string theory. There are also instantonic D(−1)-branes, which are localized in both space and time. Discovery D-branes were discovered by Jin Dai, Robert Leigh, and Joseph Polchinski, and independently by Petr Hořava, in 1989. In 1995, Polchinski identified D-branes with black p-brane solutions of supergravity, a discovery that triggered the second superstring revolution and led to both holographic and M-theory dualities. Theoretical background The equations of motion of string theory r ...
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K-theory (physics)
In string theory, K-theory classification refers to a conjectured application of K-theory (in abstract algebra and algebraic topology) to superstrings, to classify the allowed Ramond–Ramond field strengths as well as the charges of stable D-branes. In condensed matter physics K-theory has also found important applications, specially in the topological classification of topological insulators, superconductors and stable Fermi surfaces (, ). History This conjecture, applied to D-brane charges, was first proposed by . It was popularized by who demonstrated that in type IIB string theory arises naturally from Ashoke Sen's realization of arbitrary D-brane configurations as stacks of D9-brane, D9 and anti-D9-branes after tachyon condensation. Such stacks of branes are inconsistent in a non-torsion Kalb–Ramond field, Neveu–Schwarz (NS) 3-form background, which, as was highlighted by , complicates the extension of the K-theory classification to such cases. suggested a soluti ...
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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 ...
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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 ...
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Joseph Polchinski
Joseph Gerard Polchinski Jr. (; May 16, 1954 – February 2, 2018) was an American theoretical physicist and string theorist. Biography Polchinski was born in White Plains, New York, the elder of two children to Joseph Gerard Polchinski Sr. (1929–2002), a financial consultant and manager, and Joan (née Thornton), an office worker and homemaker. Polchinski was primarily of Irish descent with his paternal grandfather being Polish. Polchinski graduated from Canyon del Oro High School in Tucson, Arizona, in 1971. He obtained his B.S. degree from Caltech in 1975, and his Ph.D. from the University of California, Berkeley, in 1980 under the supervision of Stanley Mandelstam. He did not publish any papers as a graduate student. After postdoctoral positions at SLAC (1980–82) and Harvard (1982–84) he was a professor at the University of Texas at Austin from 1984 to 1992. From 1992 to March 2017 he was a professor in the Physics Department at the University of California, Santa ...
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Supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as the Minimal Supersymmetric Standard Model. Supergravity is the gauge theory of local supersymmetry. Since the supersymmetry (SUSY) generators form together with the Poincaré algebra and superalgebra, called the super-Poincaré algebra, supersymmetry as a gauge theory makes gravity arise in a natural way. Gravitons Like all covariant approaches to quantum gravity, supergravity contains a spin-2 field whose quantum is the graviton. Supersymmetry requires the graviton field to have a superpartner. This field has spin 3/2 and its quantum is the gravitino. The number of gravitino fields is equal to the number of supersymmetries. History Gauge supersymmetry The first theory of local supersymmetry was proposed by Dick Arnowitt and Pra ...
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Tachyon Condensation
Tachyon condensation is a process in particle physics in which a system can lower its potential energy by spontaneously producing particles. The end result is a "condensate" of particles that fills the volume of the system. Tachyon condensation is closely related to second-order phase transitions. Technical overview Tachyon condensation is a process in which a tachyonic field—usually a Scalar field theory, scalar field—with a complex number, complex mass acquires a vacuum expectation value and reaches the minimum of the potential energy. While the field is tachyonic and unstable near the local maximum of the potential, the field gets a non-negative squared mass and becomes stable near the minimum. The appearance of tachyons is a potentially serious problem for any theory; examples of tachyonic fields amenable to condensation are all cases of spontaneous symmetry breaking. In condensed matter physics a notable example is ferromagnetism; in particle physics the best known ...
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Second Superstring Revolution
The history of string theory spans several decades of intense research including two superstring revolutions. Through the combined efforts of many researchers, string theory has developed into a broad and varied subject with connections to quantum gravity, particle and condensed matter physics, cosmology, and pure mathematics. 1943–1959: S-matrix theory String theory represents an outgrowth of S-matrix theory, a research program begun by Werner Heisenberg in 1943 following John Archibald Wheeler's 1937 introduction of the S-matrix. Many prominent theorists picked up and advocated S-matrix theory, starting in the late 1950s and throughout the 1960s. The field became marginalized and discarded in the mid-1970s and disappeared in the 1980s. Physicists neglected it because some of its mathematical methods were alien, and because quantum chromodynamics supplanted it as an experimentally better-qualified approach to the strong interactions. The theory presented a radical rethinkin ...
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String (physics)
In physics, a string is a physical entity postulated in string theory and related subjects. Unlike elementary particles, which are zero-dimensional or point-like by definition, strings are one-dimensional extended entities. Researchers often have an interest in string theories because theories in which the fundamental entities are strings rather than point particles automatically have many properties that some physicists expect to hold in a fundamental theory of physics. Most notably, a theory of strings that evolve and interact according to the rules of quantum mechanics will automatically describe quantum gravity. Overview In string theory, the strings may be open (forming a segment with two endpoints) or closed (forming a loop like a circle) and may have other special properties. Prior to 1995, there were five known versions of string theory incorporating the idea of supersymmetry (these five are known as superstring theories) and two versions without supersymmetry known as ...
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Robert Leigh (physicist)
Robert Graham Leigh is a Canadian physicist working on string theory. Biography Leigh obtained his B.Sc. degree from the University of Guelph in 1986, and his Ph.D. from the University of Texas at Austin in 1991, working with Joe Polchinski. After postdoctoral positions at Santa Cruz and Rutgers, he has been a professor at the University of Illinois at Urbana-Champaign since 1996. Since 2007, he has been a Fellow of the American Physical Society.APS Fellow listing
retrieved 2014-12-14. Leigh discovered, in association with Jin Dai and , an important class of extended objects in



Black P-brane
In general relativity, a black brane is a solution of the Einstein field equations that generalizes a black hole solution but it is also extended—and translationally symmetric—in additional spatial dimensions. That type of solution would be called a black -brane. In string theory, the term black brane describes a group of D1-branes that are surrounded by a horizon. With the notion of a horizon in mind as well as identifying points as zero-branes, a generalization of a black hole is a black p-brane. However, many physicists tend to define a black brane separate from a black hole, making the distinction that the singularity of a black brane is not a point like a black hole, but instead a higher dimensional object. A BPS black brane is similar to a BPS black hole. They both have electric charges. Some BPS black branes have magnetic charges. The metric for a black -brane in a -dimensional spacetime is: ^ = \left( \eta_ + \frac u_a u_b \right) d \sigma^a d \sigma^b + \left ...
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Type II String Theory
In theoretical physics, type II string theory is a unified term that includes both type IIA strings and type IIB strings theories. Type II string theory accounts for two of the five consistent superstring theories in ten dimensions. Both theories have \mathcal=2 extended supersymmetry which is maximal amount of supersymmetry — namely 32 supercharges — in ten dimensions. Both theories are based on oriented closed strings. On the worldsheet, they differ only in the choice of GSO projection. They were first discovered by Michael Green and John Henry Schwarz in 1982, with the terminology of type I and type II coined to classify the three string theories known at the time. Type IIA string theory At low energies, type IIA string theory is described by type IIA supergravity in ten dimensions which is a non-chiral theory (i.e. left–right symmetric) with (1,1) ''d''=10 supersymmetry; the fact that the anomalies in this theory cancel is therefore trivial. In the 1990 ...
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Ashoke Sen
Ashoke Sen FRS (; born 1956) is an Indian theoretical physicist and distinguished professor at the International Centre for Theoretical Sciences (ICTS), Bangalore. A former distinguished professor at the Harish-Chandra Research Institute, Prayagraj, He is also an honorary fellow in National Institute of Science Education and Research (NISER) India. He is also a Morningstar Visiting professor at MIT and a distinguished professor at the Korea Institute for Advanced Study. His main area of work is string theory. He was among the first recipients of the Breakthrough Prize in Fundamental Physics "for opening the path to the realization that all string theories are different limits of the same underlying theory". Early life He was born on 15 July 1956 in Kolkata, and is the elder son of Anil Kumar Sen, a former professor of physics at the Scottish Church College, Kolkata, and Gouri Sen, a homemaker. After completing his schooling from Sailendra Sircar Vidyalaya in Kolkata, he ...
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