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GSO Projection
The GSO projection (named after Ferdinando Gliozzi, Joël Scherk, and David I. Olive) F. Gliozzi, J. Scherk and D. I. Olive, "Supersymmetry, Supergravity Theories and the Dual Spinor Model", ''Nucl. Phys. B'' 122 (1977), 253. is an ingredient used in constructing a consistent model in superstring theory. The projection is a selection of a subset of possible vertex operators in the worldsheet conformal field theory (CFT)—usually those with specific worldsheet fermion number and periodicity conditions. Such a projection is necessary to obtain a consistent worldsheet CFT. For the projection to be consistent, the set ''A'' of operators retained by the projection must satisfy: * Closure — The operator product expansion (OPE) of any two operators in ''A'' contains only operators which are in ''A''. * Mutual locality — There are no branch cuts in the OPE of any two operators in the set ''A''. * Modular invariance — The partition function on the two-torus of the theory cont ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ferdinando Gliozzi
Ferdinando Gliozzi (; born 1940) is a string theorist at the Istituto Nazionale di Fisica Nucleare. Along with David Olive and Joël Scherk, he proposed the GSO projection to map out the tachyon A tachyon () or tachyonic particle is a hypothetical particle that always travels faster than light. Physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such partic ...ic states in the Neveu–Schwarz sector. References Italian string theorists Living people 1940 births {{Italy-physicist-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branch Cut
In the mathematical field of complex analysis, a branch point of a multi-valued function (usually referred to as a "multifunction" in the context of complex analysis) is a point such that if the function is n-valued (has n values) at that point, all of its neighborhoods contain a point that has more than n values. Multi-valued functions are rigorously studied using Riemann surfaces, and the formal definition of branch points employs this concept. Branch points fall into three broad categories: algebraic branch points, transcendental branch points, and logarithmic branch points. Algebraic branch points most commonly arise from functions in which there is an ambiguity in the extraction of a root, such as solving the equation ''w''2 = ''z'' for ''w'' as a function of ''z''. Here the branch point is the origin, because the analytic continuation of any solution around a closed loop containing the origin will result in a different function: there is non-trivial monodromy. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Supersymmetry
In a supersymmetric theory the equations for force and the equations for matter are identical. In theoretical and mathematical physics, any theory with this property has the principle of supersymmetry (SUSY). Dozens of supersymmetric theories exist. Supersymmetry is a spacetime symmetry between two basic classes of particles: bosons, which have an integer-valued spin and follow Bose–Einstein statistics, and fermions, which have a half-integer-valued spin and follow Fermi–Dirac statistics. In supersymmetry, each particle from one class would have an associated particle in the other, known as its superpartner, the spin of which differs by a half-integer. For example, if the electron exists in a supersymmetric theory, then there would be a particle called a ''"selectron"'' (superpartner electron), a bosonic partner of the electron. In the simplest supersymmetry theories, with perfectly " unbroken" supersymmetry, each pair of superpartners would share the same mass and intern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tachyon
A tachyon () or tachyonic particle is a hypothetical particle that always travels faster than light. Physicists believe that faster-than-light particles cannot exist because they are not consistent with the known laws of physics. If such particles did exist they could be used to send signals faster than light. According to the theory of relativity this would violate causality, leading to logical paradoxes such as the grandfather paradox. Tachyons would exhibit the unusual property of increasing in speed as their energy decreases, and would require infinite energy to slow down to the speed of light. No verifiable experimental evidence for the existence of such particles has been found. In the 1967 paper that coined the term, Gerald Feinberg proposed that tachyonic particles could be made from excitations of a quantum field with imaginary mass. However, it was soon realized that Feinberg's model did not in fact allow for superluminal (faster-than-light) particles or signals and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Toy Model
In the modeling of physics, a toy model is a deliberately simplistic model with many details removed so that it can be used to explain a mechanism concisely. It is also useful in a description of the fuller model. * In "toy" mathematical models, this is usually done by reducing or extending the number of dimensions or reducing the number of fields/variables or restricting them to a particular symmetric form. * In Macroeconomics modelling, are a class of models, some may be only loosely based on theory, others more explicitly so. But they have the same purpose. They allow for a quick first pass at some question, and present the essence of the answer from a more complicated model or from a class of models. For the researcher, they may come before writing a more elaborate model, or after, once the elaborate model has been worked out. Blanchard list of examples includes IS–LM model, the Mundell–Fleming model, the RBC model, and the New Keynesian model. * In "toy" physical descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type 0 String Theory
The Type 0 string theory is a less well-known model of string theory. It is a superstring theory in the sense that the worldsheet theory is supersymmetric. However, the spacetime spectrum is not supersymmetric and, in fact, does not contain any fermions at all. In dimensions greater than two, the ground state is a tachyon so the theory is unstable. These properties make it similar to the bosonic string and an unsuitable proposal for describing the world as we observe it, although a GSO projection does get rid of the tachyon and the even G-parity sector of the theory defines a stable string theory. The theory is used sometimes as a toy model for exploring concepts in string theory, notably closed string tachyon condensation. Some other recent interest has involved the two-dimensional Type 0 string which has a non-perturbatively stable matrix model description. Like the Type II string, different GSO projection The GSO projection (named after Ferdinando Gliozzi, Joël Scherk, and Da ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the 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. 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 1990s it was realized by Edward Witten (building on previous insights by Michael Duff, Paul Townsend, and others) that the limit of type IIA string theory in which the string coupling goes to infinity becomes a new 11-dimensional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur. Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The physicist Albert Einstein helped develop the idea of spacetime as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Einstein based a work on special relativity on two postulates: * The laws of physics are invariant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modular Invariance
In theoretical physics, modular invariance is the invariance under the group such as SL(2,Z) of large diffeomorphisms of the torus. The name comes from the classical name modular group of this group, as in modular form theory. In string theory, modular invariance is an additional requirement for one-loop diagrams. This helps in getting rid of some global anomalies such as the gravitational anomalies. Equivalently, in two-dimensional conformal field theory A two-dimensional conformal field theory is a quantum field theory on a Euclidean two-dimensional space, that is invariant under local conformal transformations. In contrast to other types of conformal field theories, two-dimensional conformal fie ... the torus partition function must be invariant under the modular group SL(2,Z). String theory Symmetry {{theoretical-physics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two-torus
In geometry, a torus (plural tori, colloquially donut or doughnut) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis that is coplanar with the circle. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution. If the axis of revolution is tangent to the circle, the surface is a horn torus. If the axis of revolution passes twice through the circle, the surface is a spindle torus. If the axis of revolution passes through the center of the circle, the surface is a degenerate torus, a double-covered sphere. If the revolved curve is not a circle, the surface is called a ''toroid'', as in a square toroid. Real-world objects that approximate a torus of revolution include swim rings, inner tubes and ringette rings. Eyeglass lenses that combine spherical and cylindrical correction are toric lenses. A torus should not be confused with a '' solid torus'', which is formed by r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Operator Product Expansion
In quantum field theory, the operator product expansion (OPE) is used as an axiom to define the product of fields as a sum over the same fields. As an axiom, it offers a non-perturbative approach to quantum field theory. One example is the vertex operator algebra, which has been used to construct two-dimensional conformal field theories. Whether this result can be extended to QFT in general, thus resolving many of the difficulties of a perturbative approach, remains an open research question. In practical calculations, such as those needed for scattering amplitudes in various collider experiments, the operator product expansion is used in QCD sum rules to combine results from both perturbative and non-perturbative (condensate) calculations. 2D Euclidean quantum field theory In 2D Euclidean field theory, the operator product expansion is a Laurent series expansion associated to two operators. A Laurent series is a generalization of the Taylor series in that finitely many powers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Joël Scherk
Joël Scherk (; 27 May 1946 – 16 May 1980) was a French theoretical physicist who studied string theory and supergravity. Work Scherk studied in Paris at the École Normale Supérieure (ENS). In 1969 he received his diploma (Thèse de troisième cycle) at University of Paris XI in Orsay with and Claude Bouchiat and in 1971 he completed his doctorate (Doctorat d'État) at the same time as his colleague André Neveu. In 1974, together with John H. Schwarz, Scherk realised that string theory was a theory of quantum gravity. In 1978, together with Eugène Cremmer and Bernard Julia, Scherk constructed the Lagrangian and supersymmetry transformations for supergravity in eleven dimensions, which is one of the foundations of M-theory. He died unexpectedly, and in tragic circumstances, months after the supergravity workshop at the State University of New York at Stony Brook that was held on 27–29 September 1979. The workshop proceedings were dedicated to his memory, with a statemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
