|
M2-brane
In theoretical physics, an M2-brane, is a spatially extended mathematical object (brane) that appears in string theory and in related theories (e.g. M-theory, F-theory). In particular, it is a solution of eleven-dimensional supergravity which possesses a three-dimensional world volume. Description The M2-brane solution can be found by requiring (Poincare)_\times SO(8) symmetry of the solution and solving the supergravity equations of motion with the p-brane ansatz. The solution is given by a metric and three- form gauge field which, in isotropic coordinates, can be written as : \begin ds^_ &= \left(1+\frac\right)^dx^ dx^\eta_ + \left(1+\frac\right)^dx^dx^\delta_ \\ F_ &= \epsilon_ \partial_\left(1+\frac\right)^, \quad \mu=1,\ldots ,3 \quad i=4,\ldots , 11,\end where \eta is the flat-space metric and the distinction has been made between world volume x^\mu and transverse x^i coordinates. The constant q is proportional to the charge of the brane which is given by the integral o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eleven-dimensional Supergravity
In supersymmetry, eleven-dimensional supergravity is the theory of supergravity in the highest number of dimensions allowed for a supersymmetric theory. It contains a graviton, a gravitino, and a 3-form gauge field, with their interactions uniquely fixed by supersymmetry. Discovered in 1978 by Eugène Cremmer, Bernard Julia, and Joël Scherk, it quickly became a popular candidate for a theory of everything during the 1980s. However, interest in it soon faded due to numerous difficulties that arise when trying to construct physically realistic models. It came back to prominence in the mid-1990s when it was found to be the low energy limit of M-theory, making it crucial for understanding various aspects of string theory. History Supergravity was discovered in 1976 through the construction of pure four-dimensional supergravity with one gravitino. One important direction in the supergravity program was to try to construct four-dimensional \mathcal N = 8 supergravity since thi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brane
In string theory and related theories (such as supergravity), a brane is a physical object that generalizes the notion of a zero-dimensional point particle, a one-dimensional string, or a two-dimensional membrane to higher-dimensional objects. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. Mathematically, branes can be represented within categories, and are studied in pure mathematics for insight into homological mirror symmetry and noncommutative geometry. The word "brane" originated in 1987 as a contraction of " membrane". ''p''-branes A point particle is a 0-brane, of dimension zero; a string, named after vibrating musical strings, is a 1-brane; a membrane, named after vibrating membranes such as drumheads, is a 2-brane. The corresponding object of arbitrary dimension ''p'' is called a ''p''-brane, a term coined by M. J. Duff ''et al. ... [...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] |
P-brane
In string theory and related theories (such as supergravity), a brane is a physical object that generalizes the notion of a zero- dimensional point particle, a one-dimensional string, or a two-dimensional membrane to higher-dimensional objects. Branes are dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as charge. Mathematically, branes can be represented within categories, and are studied in pure mathematics for insight into homological mirror symmetry and noncommutative geometry. The word "brane" originated in 1987 as a contraction of " membrane". ''p''-branes A point particle is a 0-brane, of dimension zero; a string, named after vibrating musical strings, is a 1-brane; a membrane, named after vibrating membranes such as drumheads, is a 2-brane. The corresponding object of arbitrary dimension ''p'' is called a ''p''-brane, a term coined by M. J. Duff ''et a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Membrane (M-theory)
In string theory and related theories (such as supergravity), a brane is a physical object that generalizes the notion of a zero-dimensional point particle, a one-dimensional String (physics), string, or a two-dimensional membrane to higher-dimensional objects. Branes are dynamical system, dynamical objects which can propagate through spacetime according to the rules of quantum mechanics. They have mass and can have other attributes such as Charge (physics) , charge. Mathematically, branes can be represented within Category (mathematics) , categories, and are studied in pure mathematics for insight into homological mirror symmetry and noncommutative geometry. The word "brane" originated in 1987 as a contraction of "membrane". ''p''-branes A point particle is a 0-brane, of dimension zero; a string, named after vibrating string (music), musical strings, is a 1-brane; a membrane, named after acoustic membrane, vibrating membranes such as drumheads, is a 2-brane. The correspond ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Physics
Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain, and predict List of natural phenomena, natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigour while giving little weight to experiments and observations.There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics. For example, while developing special relativity, Albert E ... [...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] |
F-theory
In theoretical physics, F-theory is a branch of string theory developed by Iranian-American physicist Cumrun Vafa. The new vacua described by F-theory were discovered by Vafa and allowed string theorists to construct new realistic vacua — in the form of F-theory compactified on elliptically fibered Calabi–Yau four-folds. The letter "F" supposedly stands for "Father" in relation to "Mother"-theory. Compactifications F-theory is formally a 12-dimensional theory, but the only way to obtain an acceptable background is to compactify this theory on a two-torus. By doing so, one obtains type IIB superstring theory in 10 dimensions. The SL(2,Z) S-duality symmetry of the resulting type IIB string theory is manifest because it arises as the group of large diffeomorphisms of the two-dimensional torus. More generally, one can compactify F-theory on an elliptically fibered manifold ( elliptic fibration), i.e. a fiber bundle whose fiber is a two-dimensional torus (also calle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
World Line
The world line (or worldline) of an object is the path that an object traces in 4-dimensional spacetime. It is an important concept of modern physics, and particularly theoretical physics. The concept of a "world line" is distinguished from concepts such as an "orbit" or a " trajectory" (e.g., a planet's ''orbit in space'' or the ''trajectory'' of a car on a road) by inclusion of the dimension ''time'', and typically encompasses a large area of spacetime wherein paths which are straight perceptually are rendered as curves in spacetime to show their (relatively) more absolute position states—to reveal the nature of special relativity or gravitational interactions. The idea of world lines was originated by physicists and was pioneered by Hermann Minkowski. The term is now used most often in the context of relativity theories (i.e., special relativity and general relativity). Usage in physics A world line of an object (generally approximated as a point in space, e.g., a p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metric Tensor (general Relativity)
In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study. The metric captures all the geometric and causal structure of spacetime, being used to define notions such as time, distance, volume, curvature, angle, and separation of the future and the past. In general relativity, the metric tensor plays the role of the gravitational potential in the classical theory of gravitation, although the physical content of the associated equations is entirely different. Gutfreund and Renn say "that in general relativity the gravitational potential is represented by the metric tensor." Notation and conventions This article works with a metric signature that is mostly positive (); see sign convention. The gravitation constant G will be kept explicit. This article employs the Einstein summation convention, where repeated indices are automatically summed over. Definition Mathematically, spacetime is represented by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Form
In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, especially in geometry, topology and physics. For instance, the expression f(x) \, dx is an example of a -form, and can be integrated over an interval ,b/math> contained in the domain of f: \int_a^b f(x)\,dx. Similarly, the expression f(x,y,z) \, dx \wedge dy + g(x,y,z) \, dz \wedge dx + h(x,y,z) \, dy \wedge dz is a -form that can be integrated over a surface S: \int_S \left(f(x,y,z) \, dx \wedge dy + g(x,y,z) \, dz \wedge dx + h(x,y,z) \, dy \wedge dz\right). The symbol \wedge denotes the exterior product, sometimes called the ''wedge product'', of two differential forms. Likewise, a -form f(x,y,z) \, dx \wedge dy \wedge dz represents a volume element that can be integrated over a region of space. In general, a -form is an object ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
