|
Conformal Bootstrap
The conformal bootstrap is a non-perturbative mathematical method to constrain and solve conformal field theories, i.e. models of particle physics or statistical physics that exhibit similar properties at different levels of resolution. Overview Unlike more traditional techniques of quantum field theory, conformal bootstrap does not use the Lagrangian of the theory. Instead, it operates with the general axiomatic parameters, such as the scaling dimensions of the local operators and their operator product expansion coefficients. A key axiom is that the product of local operators must be expressible as a sum over local operators (thus turning the product into an algebra); the sum must have a non-zero radius of convergence. This leads to decompositions of correlation functions into structure constants and conformal blocks. The main ideas of the conformal bootstrap were formulated in the 1970s by the Soviet physicist Alexander Polyakov and the Italian physicists Sergio Ferrara, R ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-perturbative
In mathematics and physics, a non-perturbative function or process is one that cannot be described by perturbation theory. An example is the function : f(x) = e^, which does not have a Taylor series at ''x'' = 0. Every coefficient of the Taylor expansion around ''x'' = 0 is exactly zero, but the function is non-zero if ''x'' ≠ 0. In physics, such functions arise for phenomena which are impossible to understand by perturbation theory, at any finite order. In quantum field theory, 't Hooft–Polyakov monopoles, domain walls, flux tubes, and instantons are examples. A concrete, physical example is given by the Schwinger effect, whereby a strong electric field may spontaneously decay into electron-positron pairs. For not too strong fields, the rate per unit volume of this process is given by, : \Gamma = \frac \mathrm^ which cannot be expanded in a Taylor series in the electric charge e, or the electric field strength E. Here m is the mass of an electron and we have used units ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alexander Belavin
Alexander "Sasha" Abramovich Belavin (russian: Алекса́ндр Абра́мович Бела́вин, born 1942) is a Russian physicist, known for his contributions to string theory. He is a professor at the Independent University of Moscow and а researcher at the Landau Institute for Theoretical Physics. He is also a member of the editorial board of the Moscow Mathematical Journal. Work Belavin participated in the discovery of the BPST instanton (1975) which aided the understanding of the chiral anomaly and gave new directions within quantum field theory. With G. Avdeeva he showed evidence of new coupling regimes for gauge field theory (1973). He also developed the Belavin S-matrices, exactly solvable models in two-dimensional relativistic theories (1981). He co-authored the BPZ paper (1984) with Alexander Polyakov and Alexander Zamolodchikov on two-dimensional conformal field theory, which became important for string theory. With Vadim Knizhnik he obtained the Belavin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ising Critical Exponents
This article lists the critical exponents of the ferromagnetic transition in the Ising model. In statistical physics, the Ising model is the simplest system exhibiting a continuous phase transition with a scalar order parameter and \mathbb_2 symmetry. The critical exponents of the transition are universal values and characterize the singular properties of physical quantities. The ferromagnetic transition of the Ising model establishes an important universality class, which contains a variety of phase transitions as different as ferromagnetism close to the Curie point and critical opalescence of liquid near its critical point. From the quantum field theory point of view, the critical exponents can be expressed in terms of scaling dimensions of the local operators \sigma,\epsilon,\epsilon' of the conformal field theory describing the phase transition (In the Ginzburg–Landau description, these are the operators normally called \phi,\phi^2,\phi^4.) These expressions are given in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ising Model
The Ising model () (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors. Neighboring spins that agree have a lower energy than those that disagree; the system tends to the lowest energy but heat disturbs this tendency, thus creating the possibility of different structural phases. The model allows the identification of phase transitions as a simplified model of reality. The two-dimensional square-lattice Ising model is one of the simplest statistical models to show a phase transition. The Ising model was invented by the physicist , who gave it as a prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Critical Point (thermodynamics)
In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a ''critical temperature'' ''T''c and a ''critical pressure'' ''p''c, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures, and the ferromagnet–paramagnet transition (Curie temperature) in the absence of an external magnetic field. Liquid–vapor critical point Overview For simplicity and clarity, the generic notion of ''critical point'' is best introduced by discussing a specific example, the vapor–liquid critical point. This was the first critical point to be discovered, and it is still the best known and most studied one. The figu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Superconformal Algebra
In theoretical physics, the superconformal algebra is a graded Lie algebra or superalgebra that combines the conformal algebra and supersymmetry. In two dimensions, the superconformal algebra is infinite-dimensional. In higher dimensions, superconformal algebras are finite-dimensional and generate the superconformal group (in two Euclidean dimensions, the Lie superalgebra does not generate any Lie supergroup). Superconformal algebra in dimension greater than 2 The conformal group of the (p+q)-dimensional space \mathbb^ is SO(p+1,q+1) and its Lie algebra is \mathfrak(p+1,q+1). The superconformal algebra is a Lie superalgebra containing the bosonic factor \mathfrak(p+1,q+1) and whose odd generators transform in spinor representations of \mathfrak(p+1,q+1). Given Kač's classification of finite-dimensional simple Lie superalgebras, this can only happen for small values of p and q. A (possibly incomplete) list is * \mathfrak^*(2N, 2,2) in 3+0D thanks to \mathfrak(2,2)\simeq\math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alessandro Vichi
Alessandro is both a given name and a surname, the Italian form of the name Alexander. Notable people with the name include: People with the given name Alessandro * Alessandro Allori (1535–1607), Italian portrait painter * Alessandro Baricco (born 1958), Italian novelist * Alessandro Bega (born 1991), Italian tennis player * Alessandro Bordin (born 1998), Italian footballer * Alessandro Botticelli (1445–1510), Italian painter * Alessandro Bovo (born 1969), Italian water polo player * Alessandro Cagliostro (1743–1795), alias of occultist and adventurer Giuseppe Balsamo * Alessandro Calcaterra (born 1975), Italian water polo player * Alessandro Calvi (born 1983), Italian swimmer * Alessandro Cattelan (born 1980), Italian television preesenter * Alessandro Cortini (born 1976), Italian musician * Alessandro Criscuolo (1937–2020), Italian judge * Alessandro Del Piero (born 1974), Italian footballer * Alessandro Di Munno (born 2000), Italian footballer * Alessandro Evangelisti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Slava Rychkov
Vyacheslav Rychkov (called Slava Rychkov, Russian Вячеслав Рычков, transcription Vyacheslav Rychkov; born 27 May 1975 in Samara, Russia ) is a Russian-Italian-French theoretical physicist and mathematician. Career In 1996, Rychkov obtained his diploma (B.S., M.S.) from the Moscow Institute of Physics and Technology. From 1996 to 1998 he studied at the University of Jena. He received his doctorate in mathematics from Princeton University, under the supervision of Elias Stein, in 2002 with a thesis titled "Estimates for Oscillatory Integral Operators". Alexander Polyakov was his unofficial supervisor. He was a post-doctoral fellow at the University of Amsterdam (2002-2005) and at the Scuola Normale Superiore in Pisa, where he became assistant professor in 2007. In 2009 he became a professor of physics at the University of Paris VI and a member of the Laboratory of Theoretical Physics at the École Normale Supérieure in Paris. Since 2012 to 2017 he was a staff memb ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Riccardo Rattazzi
Riccardo Rattazzi (born 1964) is an Italian theoretical physicist and a professor at the École Polytechnique Fédérale de Lausanne. His main research interests are in physics beyond the Standard Model and in cosmology. Career Riccardo Rattazzi studied physics at the Scuola Normale Superiore di Pisa and at the University of Pisa, where he received the Laurea cum laude in 1987. He carried out graduate research at the Scuola Normale Superiore di Pisa under the guidance of Riccardo Barbieri. He held postdoctoral positions at the University of California, Berkeley (1992-1993), at the Rutgers University (1993-1996), and at CERN (1996-1998). In 1998 he became a permanent researcher at the Instituto Nazionale di Fisica Nucleare in Pisa. From 2001 to 2006 he was a junior staff member of ththeoretical physics departmentat CERN. Since 2006 he holds a professorship of physics at the École Polytechnique Fédérale de Lausanne. Main scientific discoveries In 1998, together with Gian Giu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liouville Field Theory
In physics, Liouville field theory (or simply Liouville theory) is a two-dimensional conformal field theory whose classical equation of motion is a generalization of Liouville's equation. Liouville theory is defined for all complex values of the central charge c of its Virasoro symmetry algebra, but it is unitary only if :c\in(1,+\infty), and its classical limit is : c\to +\infty. Although it is an interacting theory with a continuous spectrum, Liouville theory has been solved. In particular, its three-point function on the sphere has been determined analytically. Introduction Liouville theory describes the dynamics of a field \phi called the Liouville field, which is defined on a two-dimensional space. This field is not a free field due to the presence of an exponential potential : V(\phi) = e^\ , where the parameter b is called the coupling constant. In a free field theory, the energy eigenvectors e^ are linearly independent, and the momentum \alpha is conserved in intera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minimal Model (physics)
In theoretical physics, a minimal model or Virasoro minimal model is a two-dimensional conformal field theory whose spectrum is built from finitely many irreducible representations of the Virasoro algebra. Minimal models have been classified and solved, and found to obey an ADE classification. The term minimal model can also refer to a rational CFT based on an algebra that is larger than the Virasoro algebra, such as a W-algebra. Relevant representations of the Virasoro algebra Representations In minimal models, the central charge of the Virasoro algebra takes values of the type : c_ = 1 - 6 \ . where p, q are coprime integers such that p,q \geq 2. Then the conformal dimensions of degenerate representations are : h_ = \frac\ , \quad \text\ r,s\in\mathbb^*\ , and they obey the identities : h_ = h_ = h_\ . The spectrums of minimal models are made of irreducible, degenerate lowest-weight representations of the Virasoro algebra, whose conformal dimensions are of the type h_ with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
