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GSO Projection
The Gliozzi–Scherk–Olive (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- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 tachyonic states State most commonly refers to: * State (polity), a centralized political organization that regulates law and society within a territory **Sovereign state, a sovereign polity in international law, commonly referred to as a country **Nation state, a ... in the Neveu–Schwarz sector. References Italian string theorists Living people 1940 births {{Italy-physicist-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Branch Cut
In the mathematical field of complex analysis, a branch point of a multivalued function 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. Despite the algebraic branch point, the function w is well-defined as a multiple-valued function and, in an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Supersymmetry
Supersymmetry is a Theory, theoretical framework in physics that suggests the existence of a symmetry between Particle physics, particles with integer Spin (physics), spin (''bosons'') and particles with half-integer spin (''fermions''). It proposes that for every known particle, there exists a partner particle with different spin properties. There have been multiple experiments on supersymmetry that have failed to provide evidence that it exists in nature. If evidence is found, supersymmetry could help explain certain phenomena, such as the nature of dark matter and the hierarchy problem in particle physics. A supersymmetric theory is a theory in which the equations for force and the equations for matter are identical. In theoretical physics, theoretical and mathematical physics, any theory with this property has the ''principle of supersymmetry'' (SUSY). Dozens of supersymmetric theories exist. In theory, supersymmetry is a type of Spacetime symmetries, spacetime symmetry betwe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Tachyon
A tachyon () or tachyonic particle is a hypothetical particle that always travels Faster-than-light, faster than light. Physicists posit that faster-than-light particles cannot exist because they are inconsistent with the known Scientific law#Laws of physics, laws of physics. If such particles did exist they perhaps could be used to send signals faster than light and into the past. According to the theory of relativity this would violate Causality (physics), 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 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 theory, quantum field with imaginary mass. However, it was soon realiz ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Toy Model
A toy or plaything is an object that is used primarily to provide entertainment. Simple examples include toy blocks, board games, and dolls. Toys are often designed for use by children, although many are designed specifically for adults and pets. Toys can provide utilitarian benefits, including physical exercise, cultural awareness, or academic education. Additionally, utilitarian objects, especially those which are no longer needed for their original purpose, can be used as toys. Examples include children building a fort with empty cereal boxes and tissue paper spools, or a toddler playing with a broken TV remote. The term "toy" can also be used to refer to utilitarian objects purchased for enjoyment rather than need, or for expensive necessities for which a large fraction of the cost represents its ability to provide enjoyment to the owner, such as luxury cars, high-end motorcycles, gaming computers, and flagship smartphones. Playing with toys can be an enjoyable way of tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 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 .... Some ot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualizing and understanding relativistic effects, such as how different observers perceive ''where'' and ''when'' events occur. Until the turn of the 20th century, the assumption had been that the three-dimensional geometry of the universe (its description in terms of locations, shapes, distances, and directions) was distinct from time (the measurement of when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity. In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 the torus partition function must be invariant under the modular group SL(2,Z) In mathematics, the modular group is the projective special linear group \operatorname(2,\mathbb Z) of 2\times 2 matrices with integer coefficients and determinant 1, such that the matrices A and -A are identified. The modular group acts on th .... References String theory Symmetry {{theoretical-physics-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Two-torus
In geometry, a torus (: tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle. The main types of toruses include ring toruses, horn toruses, and spindle toruses. A ring torus is sometimes colloquially referred to as a donut or doughnut. If the axis of revolution does not touch the circle, the surface has a ring shape and is called a torus of revolution, also known as a ring torus. 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 (or ''self-crossing torus'' or ''self-intersecting 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 appro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 theory, 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. OPE Formulation and Application of Thirring model, Thirring Model are conceived by Kenneth G. Wilson. 2D Euclidean quantum field theory In 2D Euclidean field theory, the operator product expansion is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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 eleven-dimensional supergravity, 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 st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
