4D N = 1 Supergravity
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4D N = 1 Supergravity
In supersymmetry, 4D \mathcal N = 1 supergravity is the theory of supergravity in four dimensions with a single supercharge. It contains exactly one supergravity multiplet, consisting of a graviton and a gravitino, but can also have an arbitrary number of chiral and vector supermultiplets, with supersymmetry imposing stringent constraints on how these can interact. The theory is primarily determined by three functions, those being the Kähler potential, the superpotential, and the gauge kinetic matrix. Many of its properties are strongly linked to the geometry associated to the scalar fields in the chiral multiplets. After the simplest form of this supergravity was first discovered, a theory involving only the supergravity multiplet, the following years saw an effort to incorporate different matter multiplets, with the general action being derived in 1982 by Eugène Cremmer, Sergio Ferrara, Luciano Girardello, and Antonie Van Proeyen. This theory plays an important role in many Be ...
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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 ...
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Universe
The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant, and therefore all forms of matter and energy, and the structures they form, from sub-atomic particles to entire Galaxy filament, galactic filaments. Since the early 20th century, the field of cosmology establishes that space and time emerged together at the Big Bang ago and that the Expansion of the universe, universe has been expanding since then. The observable universe, portion of the universe that can be seen by humans is approximately 93 billion light-years in diameter at present, but the total size of the universe is not known. Some of the earliest Timeline of cosmological theories, cosmological models of the universe were developed by ancient Greek philosophy, ancient Greek and Indian philosophy, Indian philosophers and were geocentric model, geocentric, placing Earth at the center. Over the centuries, more prec ...
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Spinor
In geometry and physics, spinors (pronounced "spinner" IPA ) are elements of a complex numbers, complex vector space that can be associated with Euclidean space. A spinor transforms linearly when the Euclidean space is subjected to a slight (infinitesimal transformation, infinitesimal) rotation, but unlike Euclidean vector, geometric vectors and tensors, a spinor transforms to its negative when the space rotates through 360° (see picture). It takes a rotation of 720° for a spinor to go back to its original state. This property characterizes spinors: spinors can be viewed as the "square roots" of vectors (although this is inaccurate and may be misleading; they are better viewed as "square roots" of Section (fiber bundle), sections of vector bundles – in the case of the exterior algebra bundle of the cotangent bundle, they thus become "square roots" of differential forms). It is also possible to associate a substantially similar notion of spinor to Minkowski space, in which cas ...
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Majorana Fermion
In particle physics a Majorana fermion (, uploaded 19 April 2013, retrieved 5 October 2014; and also based on the pronunciation of physicist's name.) or Majorana particle is a fermion that is its own antiparticle. They were hypothesised by Ettore Majorana in 1937. The term is sometimes used in opposition to Dirac fermion, which describes fermions that are not their own antiparticles. With the exception of neutrinos, all of the Standard Model elementary fermions are known to behave as Dirac fermions at low energy (lower than the electroweak symmetry breaking temperature), and none are Majorana fermions. The nature of neutrinos is not settled – they may be either Dirac or Majorana fermions. In condensed matter physics, quasiparticle excitations can appear like bound Majorana states. However, instead of a single fundamental particle, they are the collective movement of several individual particles (themselves composite) which are governed by non-Abelian statistics. T ...
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Spin (physics)
Spin is an Intrinsic and extrinsic properties, intrinsic form of angular momentum carried by elementary particles, and thus by List of particles#Composite particles, composite particles such as hadrons, atomic nucleus, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic quantum mechanics or quantum field theory. The existence of electron spin angular momentum is inferred from experiments, such as the Stern–Gerlach experiment, in which silver atoms were observed to possess two possible discrete angular momenta despite having no orbital angular momentum. The relativistic spin–statistics theorem connects electron spin quantization to the Pauli exclusion principle: observations of exclusion imply half-integer spin, and observations of half-integer spin imply exclusion. Spin is described mathematically as a vector for some particles such as photons, and as a spinor or bispinor for other particles such as electrons. Sp ...
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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 ...
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Superspace
Superspace is the coordinate space of a theory exhibiting supersymmetry. In such a formulation, along with ordinary space dimensions ''x'', ''y'', ''z'', ..., there are also "anticommuting" dimensions whose coordinates are labeled in Grassmann numbers rather than real numbers. The ordinary space dimensions correspond to bosonic degrees of freedom, the anticommuting dimensions to fermionic degrees of freedom. The word "superspace" was first used by John Archibald Wheeler, John Wheeler in an unrelated sense to describe the Configuration space (physics), configuration space of general relativity; for example, this usage may be seen in his 1973 textbook ''Gravitation (book), Gravitation''. Informal discussion There are several similar, but not equivalent, definitions of superspace that have been used, and continue to be used in the mathematical and physics literature. One such usage is as a synonym for super Minkowski space. In this case, one takes ordinary Minkowski space, and extend ...
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Jonathan Bagger
Jonathan Anders Bagger (born August 7, 1955) is an American theoretical physicist, specializing in high energy physics and string theory and known for the Bagger–Lambert–Gustavsson action. Bagger received his bachelor's degree in 1977 from Dartmouth College. He spent the academic year 1977–1978 at the University of Cambridge as a Churchill Scholar. In 1978 he became a graduate student in physics at Princeton University, where he received his PhD in 1983. His doctoral thesis ''Matter Couplings in Supergravity Theories'' was supervised by Edward Witten. He was a postdoc from 1983 to 1986 at the Stanford Linear Accelerator Center. He was from 1986 to 1989 an associate professor at Harvard University. At Johns Hopkins University he became in 1989 a full professor, holding a professorial chair there until 2014. In 2014 he was appointed director of TRIUMF, Canada's national laboratory for particle and nuclear physics. Bagger's research deals with high-energy physics, supersymmetry ...
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Massless Particle
In particle physics, a massless particle is an elementary particle whose invariant mass is zero. At present the only confirmed massless particle is the photon. Other particles and quasiparticles Standard Model gauge bosons The photon (carrier of electromagnetism) is one of two known gauge bosons thought to be massless. The photon is well-known from direct observation to exist and be massless. The other massless gauge boson is the gluon (carrier of the strong force) whose existence has been inferred from particle collision decay products; it is expected to be massless, but a zero mass has not been confirmed by experiment. Although there are compelling theoretical reasons to believe that gluons are massless, they can never be observed as free particles due to being confined within hadrons, and hence their presumed lack of rest mass cannot be confirmed by any feasible experiment. The only other observed gauge bosons are the W and Z bosons, which are known from experiments to be ...
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Yang–Mills Theory
Yang–Mills theory is a quantum field theory for nuclear binding devised by Chen Ning Yang and Robert Mills in 1953, as well as a generic term for the class of similar theories. The Yang–Mills theory is a gauge theory based on a special unitary group , or more generally any compact Lie group. A Yang–Mills theory seeks to describe the behavior of elementary particles using these non-abelian Lie groups and is at the core of the unification of the electromagnetic force and weak forces (i.e. ) as well as quantum chromodynamics, the theory of the strong force (based on ). Thus it forms the basis of the understanding of the Standard Model of particle physics. History and qualitative description Gauge theory in electrodynamics All known fundamental interactions can be described in terms of gauge theories, but working this out took decades. Hermann Weyl's pioneering work on this project started in 1915 when his colleague Emmy Noether proved that every conserved physical ...
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Coupling (physics)
In physics, two objects are said to be coupled when they are interacting with each other. In classical mechanics, coupling is a connection between two Oscillation, oscillating systems, such as pendulums connected by a spring. The connection affects the oscillatory pattern of both objects. In particle physics, two particles are coupled if they are connected by one of the four Fundamental interaction, fundamental forces. Wave mechanics Coupled harmonic oscillator If two Waves (physics), waves are able to transmit energy to each other, then these waves are said to be "coupled." This normally occurs when the waves share a common component. An example of this is two pendulums connected by a Spring (device), spring. If the pendulums are identical, then their equations of motion are given by m\ddot = -mg\frac - k(x-y) m\ddot = -mg \frac + k(x-y) These equations represent the simple harmonic motion of the pendulum with an added coupling factor of the spring. This behavior is also see ...
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Superpartner
In particle physics, a superpartner (also sparticle) is a class of hypothetical elementary particles predicted by supersymmetry, which, among other applications, is one of the well-studied ways to extend the Standard Model of high-energy physics. When considering extensions of the Standard Model, the ''s-'' prefix from ''sparticle'' is used to form names of superpartners of the Standard Model fermions ( sfermions),Alexander I. Studenikin (ed.), ''Particle Physics in Laboratory, Space and Universe'', World Scientific, 2005, p. 327. e.g. the stop squark. The superpartners of Standard Model bosons have an ''-ino'' (bosinos) appended to their name, e.g. gluino, the set of all gauge superpartners are called the gauginos. Theoretical predictions According to the supersymmetry theory, each fermion should have a partner boson, the fermion's superpartner, and each boson should have a partner fermion. Exact ''unbroken'' supersymmetry would predict that a particle and its superpartners ...
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