This article or section is in need of attention from an expert on the subject. WikiProject Physics or the Physics Portal may be able to help recruit one. If a more appropriate WikiProject or portal exists, please adjust this template accordingly. Grand Unification is the debut album by British emo/post-hardcore quartet Fightstar. ... Image File history File links Emblem-important. ...

Grand Unification, grand unified theory, or GUT is one of several very similar unified field theories or models in physics that predicts that at extremely high energies (above 10¹⁴ GeV), the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field. ^[1] This article does not cite any references or sources. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ...

Thus far, physicists have been able to merge electromagnetism and the weak nuclear force into the electroweak force, and work is being done to merge electroweak and quantum chromodynamics into a QCD-electroweak interaction sometimes called the electrostrong force. Beyond grand unification, there is also speculation that it may be possible to merge gravity with the other three gauge symmetries into a theory of everything. Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... The weak nuclear force or weak interaction is one of the four fundamental forces of nature. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... Gravity is a force of attraction that acts between bodies that have mass. ... This article or section is in need of attention from an expert on the subject. ...

The coining of the widely-used acronym GUT has been attributed to a paper published in 1978 by Harvard University theorist Dimitri Nanopoulos (now at Texas A&M University). ^{[citation needed]} It has been suggested that this article or section be merged with Backronym and Apronym (Discuss) Acronyms and initialisms are abbreviations, such as NATO, laser, and ABC, written as the initial letter or letters of words, and pronounced on the basis of this abbreviated written form. ... Harvard redirects here. ... Professor Dimitri Nanopoulos (born 1948) is a Greek physicist. ... Texas A&M University redirects here. ...

Motivation

There is a general aesthetic among high energy physicists that the more symmetrical a theory is, the more "beautiful" and "elegant" it is. According to this aesthetic, the Standard Model gauge group, which is the direct product of three groups (modulo some finite group) is "ugly". Also, reasoning in analogy with the 19th-century unification of electricity with magnetism into electromagnetism, and especially the success of the electroweak theory, which utilizes the idea of spontaneous symmetry breaking to unify electromagnetism with the weak interaction, people wondered if it might be possible to unify all three groups in a similar manner. Physicists feel that three independent gauge coupling constants and a huge number of Yukawa coupling coefficients require far too many free parameters, and that these coupling constants ought to be explained by a theory with fewer free parameters. A gauge theory where the gauge group is a simple group only has one gauge coupling constant, and since the fermions are now grouped together in larger representations, there are fewer Yukawa coupling coefficients as well. In addition, the chiral fermion fields of the Standard Model unify into three generations of two irreducible representations () in SU(5), and three generations of an irreducible representation (16) in SO(10). This is a significant observation, as a generic combination of chiral fermions which are free of gauge anomalies will not be unified in a representation of some larger Lie group without adding additional matter fields. SO(10) also predicts a right-handed neutrino. The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... In mathematics, one can often define a direct product of objects already known, giving a new one. ... The word modulo (Latin, with respect to a modulus of ___) is the Latin ablative of modulus which itself means a small measure. ... In mathematics, a finite group is a group which has finitely many elements. ... Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... For other senses of this word, see magnetism (disambiguation). ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... In physics, the electroweak theory presents a unified description of two of the four fundamental forces of nature: electromagnetism and the weak nuclear force. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four fundamental interactions of nature. ... In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... In mathematics Representation theory is the name given to the study of standard representations of abstract mathematical structures. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... In theoretical physics, a gauge anomaly is an example of an anomaly: it is an effect of quantum mechanics - usually a one-loop diagram - that invalidates the gauge symmetry of a quantum field theory i. ... In mathematics, a Lie group, named after Norwegian mathematician Sophus Lie (IPA pronunciation: , sounds like Lee), is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. ... For other uses, see Neutrino (disambiguation). ...

GUT theory specifically predicts relations among the fermion masses, such as between the electron and the down quark, the muon and the strange quark, and the tau lepton and the bottom quark for SU(5) and SO(10). Some of these mass relations hold approximately, but most don't. See Georgi-Jarlskog mass relation. If we look at the renormalization group running of the three-gauge couplings have been found to nearly, but not quite, meet at the same point if the hypercharge is normalized so that it is consistent with SU(5)/SO(10) GUTs, which are precisely the GUT groups which lead to a simple fermion unification. This is a significant result, as other Lie groups lead to different normalizations. However, if the supersymmetric extension MSSM is used instead of the Standard Model, the match becomes much more accurate. It is commonly believed that this matching is unlikely to be a coincidence. Also, most model builders simply assume SUSY because it solves the hierarchy problem—i.e., it stabilizes the electroweak Higgs mass against radiative corrections. And the Majorana mass of the right-handed neutrino SO(10) theories with its mass set to the gauge unification scale is examined, values for the left-handed neutrino masses (see neutrino oscillation) are produced via the seesaw mechanism. These values are 10–100 times smaller than the GUT scale, but still relatively close. In particle physics, fermions are particles with half-integer spin, such as protons and electrons. ... The down quark is a first-generation quark with a charge of -(1/3)e. ... The muon (from the letter mu (μ)--used to represent it) is an elementary particle with negative electric charge and a spin of 1/2. ... The strange quark is a second-generation quark with a charge of -(1/3)e and a strangeness of −1. ... The tau lepton (often called the tau or occasionally the tauon) is a negatively charged elementary particle with a lifetime of 3×10−13 seconds and a high mass of 1777 MeV (compared to 939 MeV for protons and 0. ... The bottom quark is a third-generation quark with a charge of -(1/3)e. ... In grand unified theories of the SU(5) or SO(10) type, there is a mass relation predicted between the electron and the down quark, the muon and the strange quark and the tauon and the bottom quark called the Georgi-Jarlskog mass relations. ... This article or section is in need of attention from an expert on the subject. ... // The Minimal Supersymmetric Standard Model (MSSM) is the minimal extension to the Standard Model that realizes supersymmetry (non-minimal extensions exist). ... In theoretical physics, a hierarchy problem occurs when the fundamental parameters (couplings or masses) of some Lagrangian are vastly different (usually larger) than the parameters measured by experiment. ... Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo whereby a neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor. ... In theoretical physics, the seesaw mechanism is a mechanism to generate very small numbers from reasonable numbers and very large numbers. ...

(For a more elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.) In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. ... There is a natural connection, first discovered by Eugene Wigner, between the properties of particles, the representation theory of Lie groups and Lie algebras, and the symmetries of the universe. ...

Ingredients

A GUT model basically consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a Yang-Mills action for that connection given by an invariant symmetric bilinear form over its Lie algebra (which is specified by a coupling constant for each factor), a Higgs sector consisting of a number of scalar fields taking on values within real/complex representations of the Lie group and chiral Weyl fermions taking on values within a complex rep of the Lie group. The Lie group contains the Standard Model group and the Higgs fields acquire VEVs leading to a spontaneous symmetry breaking to the Standard Model. The Weyl fermions represent matter. Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In mathematics, a compact (topological, often understood) group is a topological group that is also a compact space. ... In mathematics, and specifically differential geometry, the connection form captures the invariant aspects of the connection on principal bundles, vector bundles and line bundles. ... Gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... Invariant may have meanings invariant (computer science), such as a combination of variables not altered in a loop invariant (mathematics), something unaltered by a transformation invariant (music) invariant (physics) conserved by system symmetry This is a disambiguation page — a navigational aid which lists other pages that might otherwise share... In mathematics, a bilinear form on a vector space V over a field F is a mapping V × V → F which is linear in both arguments. ... In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ... In particle physics, the Higgs sector is the collection of quantum fields and/or particles that are responsible for the Higgs mechanism i. ... In mathematics and theoretical physics, the idea of a representation of a Lie group plays an important role in the study of continuous symmetry. ... ... Wikipedia does not yet have an article with this exact name. ... Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ...

Proposed theories

Several such theories have been proposed, but none are currently universally accepted. An even more ambitious theory that includes all fundamental forces, including gravitation, is termed a theory of everything. Some common mainstream GUT models are: A fundamental interaction is a mechanism by which particles interact with each other, and which cannot be explained by another more fundamental interaction. ... Gravity redirects here. ... This article or section is in need of attention from an expert on the subject. ... Look up mainstream in Wiktionary, the free dictionary. ...

Not quite GUTs... In theoretical physics, the electroweak model breaks parity maximally. ... In particle physics, the Georgi-Glashow model is a particular grand unification theory (GUT) proposed by Howard Georgi and Sheldon Glashow in 1974. ... In particle physics, one of the grand unified theories (GUT) is based on the SO(10) Lie group. ... The Flipped SU(5) model is a GUT theory which states that the gauge group is [ SU(5) × U(1) ]/ and the fermions form three families, each consisting of the representations , 10-1 and 1-5. ... The Pati-Salam model is a GUT theory which states that the gauge group is either SU(4)× SU(2)L× SU(2)R or ( SU(4)× SU(2)L× SU(2)R )/Z2 and the fermions form three families, each consisting of the representations (4,2,1) and . ... Flipped SO(10) is a grand unified theory which is to standard SO(10) as flipped SU(5) is to SU(5). ... In physics, the trinification model is a GUT theory. ... SU(6) is a grand unified theory which includes the Georgi-Glashow SU(5) gauge group. ... In mathematics, E6 is the name of some Lie groups and also their Lie algebras . ... The word proportionality may have one of a number of meanings: In mathematics, proportionality is a mathematical relation between two quantities. ... In particle physics, the 331 model is an extension of the electroweak gauge symmetry from to with and the hypercharge and the electric charge where T3 and T8 are the Gell-Mann matrices of SU(3)L and β and I are parameters of the model. ... Chiral Color is a speculative model which extends quantum chromodynamics (QCD), the generally accepted theory for the strong interactions of quarks and leptons. ...

Note: These models refer to Lie algebras not to Lie groups. The Lie group could be [SU(4)×SU(2)×SU(2)]/Z₂, just to take a random example. Technicolor models are theories beyond the Standard Model (sometimes, but not always, GUTs) which do not have a scalar Higgs field. ... In particle physics, little Higgs is a refined version of the Higgs boson based on the idea that the Higgs boson is a pseudo-Goldstone boson arising from some global symmetry breaking at a TeV energy scale. ... In particle physics, preons are postulated point-like particles, conceived to be subcomponents of quarks and leptons. ... Interaction in the subatomic world: world lines of pointlike particles in the Standard Model or a world sheet swept up by closed strings in string theory String theory is a model of fundamental physics, whose building blocks are one-dimensional extended objects called strings, rather than the zero-dimensional point... M-theory is a solution proposed for the unknown theory of everything which would combine all five superstring theories and 11-dimensional supergravity together. ... Loop quantum gravity (LQG), also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the seemingly incompatible theories of quantum mechanics and general relativity. ... In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. ... In mathematics, a Lie group, named after Norwegian mathematician Sophus Lie (IPA pronunciation: , sounds like Lee), is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure. ...

The most promising candidate is SO(10).^{[citation needed]} (Minimal) SO(10) does not contain any exotic fermions (i.e. additional fermions besides the Standard Model fermions and the right-handed neutrino) and it unifies each generation into a single irreducible representation. Notice that a number of other GUT models are based upon subgroups of SO(10). They are the minimal left-right model, SU(5), flipped SU(5) and the Pati-Salam model. The GUT group E₆ contains SO(10) but models based upon it are significantly more complicated. The primary reason for studying E₆ models comes from E₈ × E₈ heterotic string theory. In particle physics, one of the grand unified theories (GUT) is based on the SO(10) Lie group. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... For other uses, see Neutrino (disambiguation). ... In mathematics, the term irreducible is used in several ways. ... In theoretical physics, the electroweak model breaks parity maximally. ... In mathematics, the special unitary group of degree n is the group of n by n unitary matrices with determinant 1 and entries from the field C of complex numbers, with the group operation that of matrix multiplication. ... The Flipped SU(5) model is a GUT theory which states that the gauge group is [ SU(5) × U(1) ]/ and the fermions form three families, each consisting of the representations , 10-1 and 1-5. ... The Pati-Salam model is a GUT theory which states that the gauge group is either SU(4)× SU(2)L× SU(2)R or ( SU(4)× SU(2)L× SU(2)R )/Z2 and the fermions form three families, each consisting of the representations (4,2,1) and . ... In physics, a heterotic string is a peculiar mixture (or hybrid) of the bosonic string and the superstring (the adjective heterotic comes from the Greek word heterosis). ...

GUT models generically predict the existence of topological defects such as monopoles, cosmic strings, domain walls, and others. None have been observed and their absence is known as the monopole problem in cosmology. In cosmology, a topological defect is a (often) stable configuration of matter predicted by some theories to form at phase transitions in the very early universe. ... In physics, magnetic monopole is a term describing a hypothetical particle that could be quickly clarified to a person familiar with magnets but not electromagnetic theory as a magnet with only one pole. In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle... A cosmic string is a hypothetical 1-dimensional topological defect in the fabric of spacetime. ... A domain wall is a theoretical 2-dimensional singularity. ... In physics, magnetic monopole is a term describing a hypothetical particle that could be quickly clarified to a person familiar with magnets but not electromagnetic theory as a magnet with only one pole. In more accurate terms, it would have net magnetic charge. Interest in the concept stems from particle... This article is about the physics subject. ...

GUT models also generically predict proton decay, although current experiments still haven't detected proton decay. This experimental limit on the proton's lifetime pretty much rules out minimal SU(5). In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, usually a neutral pion and a positron. ...

Image File history File links Proton_decay2. ... Image File history File links Proton_decay3. ... Image File history File links Download high resolution version (492x674, 325 KB) Summary I created these diagrams. ...

Some GUT theories like SU(5) and SO(10) suffer from what is called the doublet-triplet problem in that these theories predict that for each electroweak Higgs doublet, there corresponds a colored Higgs triplet field with a very small mass (small, meaning many orders of magnitude smaller than the GUT scale here). After all, if you unify quarks with leptons, the Higgs doublet would also be unified with a Higgs triplet. These triplets have not been observed, and not only that, they would cause extremely rapid proton decay (way below current experimental limits) and completely mess up the running together of the gauge coupling strengths in the renormalization group. In theoretical physics, the doublet-triplet (splitting) problem is a potential problem of some Grand Unified Theories, such as those associated with the Lie groups SU(5) and SO(10). ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... For other uses, see Quark (disambiguation). ... In physics, a lepton is a particle with spin-1/2 (a fermion) that does not experience the strong interaction (that is, the strong nuclear force). ...

Most GUT models require a threefold replication of the matter fields and as such, do not explain why there are three generations of fermions. Most GUT models also do not explain the little hierarchy between the fermion masses for different generations.

Current status

As of 2005, there is still no hard evidence that nature is described by a Grand Unified Theory. In fact, since the Higgs particle has not yet been discovered, it is not even certain if the Standard Model is fully accurate. The discovery of neutrino oscillations indicate strongly that the Standard Model is incomplete, and lead to renewed interest toward certain GUT such as SO(10). One of the few possible experimental tests of certain GUT is proton decay and also fermion masses. There are a few more special tests for supersymmetric GUT. 2005 is a common year starting on Saturday of the Gregorian calendar. ... Higgs bosons are hypothetical elementary particles predicted to exist by the Standard Model of particle physics. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvo whereby a neutrino created with a specific lepton flavor (electron, muon or tau) can later be measured to have a different flavor. ... In particle physics, proton decay is a hypothetical form of radioactive decay in which the proton decays into lighter subatomic particles, usually a neutral pion and a positron. ...

The gauge coupling strengths of QCD, the weak interaction and hypercharge seem to meet at a common length scale called the GUT scale and equal approximately to 10¹⁶ GeV, which is slightly suggestive. This interesting numerical observation is called the gauge coupling unification and it works particularly well if one assumes the existence of superpartners of the Standard Model particles. Still it is possible to achieve the same by postulating, for instance, that ordinary (non supersymmetric) SO(10) models break with an intermediate gauge scale, such as the one of Pati-Salam group. In physics, a coupling constant, usually denoted g, is a number that determines the strength of an interaction. ... Quantum chromodynamics (abbreviated as QCD) is the theory of the strong interaction (color force), a fundamental force describing the interactions of the quarks and gluons found in hadrons (such as the proton, neutron or pion). ... The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four fundamental interactions of nature. ... In particle physics, the hypercharge (represented by Y) is the sum of the baryon number B and the flavor charges: strangeness S, charm C, bottomness and topness T, although the last one can be omitted given the extremely short life of the top quark (it decays to other quarks before... In supersymmetry, it is proposed that every fermion should have a partner boson, known as its Superpartner. ...

See also

• Grand unification energy
• Fundamental interaction
• Particle physics and representation theory

The grand unification energy, or the GUT scale, is the energy level above which, it is believed, the electromagnetic force, weak force, and strong force become indistinguishable from each other. ... A fundamental interaction or fundamental force is a mechanism by which particles interact with each other, and which cannot be explained in terms of another interaction. ... There is a natural connection, first discovered by Eugene Wigner, between the properties of particles, the representation theory of Lie groups and Lie algebras, and the symmetries of the universe. ...

References

• An account of the origin of the term GUT