Grand Unified Theory

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Beyond the Standard Model Standard Model EvidenceHierarchy problem • Dark matter
Cosmological constant problem
Strong CP problem
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Grand Unified Theory
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Loop quantum gravity
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Canonical quantum gravity
Superfluid vacuum theoryThe term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at highenergy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single interaction characterized by one larger gauge symmetry and thus one unified coupling constant. In contrast, the experimentally verified Standard Model of particle physics is based on three independent interactions, symmetries and coupling constants.
Models that do not unify all interactions using one simple Lie group as the gauge symmetry, but do so using semisimple groups, can exhibit similar properties and are sometimes referred to as Grand Unified Theories as well.
Unifying gravity with the other three interactions would provide a theory of everything (TOE), rather than a GUT. Nevertheless, GUTs are often seen as an intermediate step towards a TOE.
The new particles predicted by models of grand unification cannot be observed directly at particle colliders because their masses are expected to be of the order of the socalled GUT scale, which is predicted to be just a few orders of magnitude below the Planck scale and thus far beyond the reach of currently foreseen collision experiments. Instead, effects of grand unification might be detected through indirect observations such as proton decay, electric dipole moments of elementary particles, or the properties of neutrinos.^{[1]} Some grand unified theories predict the existence of magnetic monopoles.
As of 2011^{[update]}, all GUT models which aim to be completely realistic are quite complicated, even compared to the Standard Model, because they need to introduce additional fields and interactions, or even additional dimensions of space. The main reason for this complexity lies in the difficulty of reproducing the observed fermion masses and mixing angles. Due to this difficulty, and due to the lack of any observed effect of grand unification so far, there is no generally accepted GUT model.
Unsolved problems in physics Are the three forces of the Standard Model unified at high energies? By which symmetry is this unification governed? Can Grand Unification explain the number of Fermion generations and their masses? Contents
History
Historically, the first true GUT which was based on the simple Lie group SU(5), was proposed by Howard Georgi and Sheldon Glashow in 1974.^{[2]} The Georgi–Glashow model was preceded by the Semisimple Lie algebra Pati–Salam model by Abdus Salam and Jogesh Pati,^{[3]} who pioneered the idea to unify gauge interactions.
The acronym GUT was first coined in 1978 by CERN researchers John Ellis, Andrzej Buras, Mary K. Gaillard, and Dimitri Nanopoulos, however in the final version of their paper^{[4]} they opted for the less anatomical GUM (Grand Unification Mass). Nanopoulos later that year was the first to use^{[5]} the acronym in a paper.^{[6]}
Motivation
The fact that the electric charges of electrons and protons seem to cancel each other exactly to extreme precision is essential for the existence of the macroscopic world as we know it, but this important property of elementary particles is not explained in the Standard Model of particle physics. While the description of strong and weak interactions within the Standard Model is based on gauge symmetries governed by the simple symmetry groups SU(3) and SU(2) which allow only discrete charges, the remaining component, the weak hypercharge interaction is described by an abelian symmetry U(1) which in principle allows for arbitrary charge assignments.^{[note 1]} The observed charge quantization, namely the fact that all known elementary particles carry electric charges which appear to be exact multiples of ^{1}⁄_{3} of the "elementary" charge, has led to the idea that hypercharge interactions and possibly the strong and weak interactions might be embedded in one Grand Unified interaction described by a single, larger simple symmetry group containing the Standard Model. This would automatically predict the quantized nature and values of all elementary particle charges. Since this also results in a prediction for the relative strengths of the fundamental interactions which we observe, in particular the weak mixing angle, Grand Unification ideally reduces the number of independent input parameters, but is also constrained by observations.
Grand Unification is reminiscent of the unification of electric and magnetic forces by Maxwell's theory of electromagnetism in the 19th century, but its physical implications and mathematical structure are qualitatively different.
Unification of matter particles
 For an elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.
SU(5)
Main article: SU(5) (physics)SU(5) is the simplest GUT. The smallest simple Lie group which contains the standard model, and upon which the first Grand Unified Theory was based, is
.
Such group symmetries allow the reinterpretation of several known particles as different states of a single particle field. However, it is not obvious that the simplest possible choices for the extended "Grand Unified" symmetry should yield the correct inventory of elementary particles. The fact that all currently known (2009) matter particles fit nicely into three copies of the smallest group representations of SU(5) and immediately carry the correct observed charges, is one of the first and most important reasons why people believe that a Grand Unified Theory might actually be realized in nature.
The two smallest irreducible representations of SU(5) are and . In the standard assignment, the contains the charge conjugates of the righthanded downtype quark color triplet and a lefthanded lepton isospin doublet, while the contains the six uptype quark components, the lefthanded downtype quark color triplet, and the righthanded electron. This scheme has to be replicated for each of the three known generations of matter. It is notable that the theory is anomaly free with this matter content.
The hypothetical righthanded neutrinos are not contained in any of these representations, which can explain their relative heaviness (see seesaw mechanism).
SO(10)
Main article: SO(10) (physics)The next simple Lie group which contains the standard model is
.
Here, the unification of matter is even more complete, since the irreducible spinor representation contains both the and of SU(5) and a righthanded neutrino, and thus the complete particle content of one generation of the extended standard model with neutrino masses. This is already the largest simple group which achieves the unification of matter in a scheme involving only the already known matter particles (apart from the Higgs sector).
Since different standard model fermions are grouped together in larger representations, GUTs specifically predict 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 GeorgiJarlskog mass relation).
The boson matrix for SO(10) is found by taking the 15x15 matrix from the 10+5 representation of SU(5) and adding an extra row and collumn for the right handed neutrino. The bosons are found by adding a partner to each of the 20 charged bosons (2 righthanded W bosons, 6 massive charged gluons and 12 X/Y type bosons) and adding an extra heavy neutral Zboson to make 5 neutral bosons in total. The boson matrix will have a boson or it's new partner in each row and column. These pairs combine to create the familiar 16D Dirac spinor matrices of SO(10).
E8 and Octonion Representations
It can be noted that a generation of 16 fermions can be put into the form of an Octonion with each element of the octonion being an 8vector. If the 3 generations are then put in a 3x3 hermitian matrix with certain additions for the diagonal elements then these matrices form an exceptional (grassman)Jordan algebra, which has the symmetry group of one of the exceptional Lie groups (F_{4},E_{6},E_{7}orE_{8}) depending on the details.
Because they are fermions the anticommutators of the Jordan algebra become commutators. It is known that E_{6} has subgroup O(10) and so is big enough to include the Standard Model. An E8 gauge group, for example, would have 8 neutral bosons, 120 charged bosons and 120 charged antibosons. To account for the 248 fermions in the lowest multiplet of E8, these would either have to include antiparticles (and so have Baryogenesis), have new undiscovered particles, or have gravitylike (Spin connection) bosons affecting elements of the particles spin direction. Each of these poses theoretical problems.
Unification of forces and the role of supersymmetry
The unification of forces is possible due to the energy scale dependence of parameters in quantum field theory called renormalization group running, which allows parameters with vastly different values at collider energies to converge at much higher energy scales.^{[7]}
The renormalization group running of the three gauge couplings in the Standard Model has 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) or 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. In this case, the coupling constants of the strong and electroweak interactions meet at the grand unification energy, also known as the GUT scale:
.
It is commonly believed that this matching is unlikely to be a coincidence, and is often quoted as one of the main motivations to further investigate supersymmetric theories despite the fact that no supersymmetric partner particles have been experimentally observed (March 2011). Also, most model builders simply assume supersymmetry because it solves the hierarchy problem—i.e., it stabilizes the electroweak Higgs mass against radiative corrections.^{[citation needed]}
Neutrino masses
Since Majorana masses of the righthanded neutrino are forbidden by SO(10) symmetry, SO(10) GUTs predict the Majorana masses of righthanded neutrinos to be close to the GUT scale where the symmetry is spontaneously broken in those models. In supersymmetric GUTs, this scale tends to be larger than would be desirable to obtain realistic masses of the light, mostly lefthanded neutrinos (see neutrino oscillation) via the seesaw mechanism.
Proposed theories
Several such theories have been proposed, but none is 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:
 minimal leftright model —
 Georgi–Glashow model —
 SO(10)
 Flipped SU(5) —
 PatiSalam model —
 flipped SO(10) —
Not quite GUTs:
Note: These models refer to Lie algebras not to Lie groups. The Lie group could be [SU(4)×SU(2)×SU(2)]/Z_{2}, just to take a random example.
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 righthanded neutrino), and it unifies each generation into a single irreducible representation. A number of other GUT models are based upon subgroups of SO(10). They are the minimal leftright model, SU(5), flipped SU(5) and the PatiSalam model. The GUT group E_{6} contains SO(10), but models based upon it are significantly more complicated. The primary reason for studying E_{6} models comes from E_{8} × E_{8} heterotic string theory.
GUT models generically predict the existence of topological defects such as monopoles, cosmic strings, domain walls, and others. But none have been observed. Their absence is known as the monopole problem in cosmology. Most GUT models also predict proton decay, although not the PatiSalam model; current experiments still haven't detected proton decay. This experimental limit on the proton's lifetime pretty much rules out minimal SU(5).
Some GUT theories like SU(5) and SO(10) suffer from what is called the doublettriplet problem. These theories predict that for each electroweak Higgs doublet, there is a corresponding colored Higgs triplet field with a very small mass (many orders of magnitude smaller than the GUT scale here). In theory, unifying quarks with leptons, the Higgs doublet would also be unified with a Higgs triplet. Such triplets have not been observed. They would also cause extremely rapid proton decay (far below current experimental limits) and prevent the gauge coupling strengths from running together in the renormalization group.
Most GUT models require a threefold replication of the matter fields. As such, they do not explain why there are three generations of fermions. Most GUT models also fail to explain the little hierarchy between the fermion masses for different generations.
Ingredients
A GUT model basically consists of a gauge group which is a compact Lie group, a connection form for that Lie group, a YangMills 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.
Current status
As of 2011^{[update]}, there is still no hard evidence that nature is described by a Grand Unified Theory. Moreover, since the Higgs particle has not yet been observed, the smaller electroweak unification is still pending.^{[8]} The discovery of neutrino oscillations indicates that the Standard Model is incomplete and has led 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.
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 10^{16} 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 PatiSalam group.
See also
 Paradigm shift
 Classical unified field theories
 X and Y bosons
 BL quantum number
Notes
 ^ There are however certain constraints on the choice of particle charges from theoretical consistency, in particular anomaly cancellation.
References
 ^ Ross, G. (1984). Grand Unified Theories. Westview Press. ISBN 9780805369687.
 ^ Georgi, H.; Glashow, S.L. (1974). "Unity of All Elementary Particle Forces". Physical Review Letters 32: 438–441. Bibcode 1974PhRvL..32..438G. doi:10.1103/PhysRevLett.32.438.
 ^ Pati, J.; Salam, A. (1974). "Lepton Number as the Fourth Color". Physical Review D 10: 275–289. Bibcode 1974PhRvD..10..275P. doi:10.1103/PhysRevD.10.275.
 ^ Buras, A.J.; Ellis, J.; Gaillard, M.K.; Nanopoulos, D.V. (1978). "Aspects of the grand unification of strong, weak and electromagnetic interactions". Nuclear Physics B 135 (1): 66–92. Bibcode 1978NuPhB.135...66B. doi:10.1016/05503213(78)902146. http://cdsweb.cern.ch/record/132734/files/197712054.pdf. Retrieved 20110321.
 ^ Nanopoulos, D.V. (1979). "Protons Are Not Forever". Orbis Scientiae 1: 91. Harvard Preprint HUTP78/A062. http://wwwspires.fnal.gov/spires/find/hep/www?rawcmd=r+HUTP78A062.
 ^ Ellis, J. (2002). "Physics gets physical". Nature 415 (6875): 957. doi:10.1038/415957b.
 ^ Ross, G. (1984). Grand Unified Theories. Westview Press. ISBN 9780805369687.
 ^ Hawking, S.W. (1996). A Brief History of Time: The Updated and Expanded Edition. (2nd ed.). Bantam Books. p. XXX. ISBN 0553380168.
Further reading
 Stephen Hawking, A Brief History of Time, includes a brief popular overview.
External links
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grand unified theory — grand unified theory, grand unification theory grand unification theory . (Theoretical physics) Any of a class of physics theories that attempts to explain the electroweak forces, stong force, and gravitation within a single mathematical… … The Collaborative International Dictionary of English
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Grand Unified Theory — Grande unification Pour les articles homonymes, voir GUT. En physique théorique, une théorie de grande unification, encore appelée GUT (pour Grand Unified Theory en anglais) désigne un modèle étendant le modèle standard de la physique des… … Wikipédia en Français
grand unified theory — or grand unification theory (GUT) Theory that attempts to unify the electroweak force (see electroweak theory) with the strong force. The unification of all four fundamental interactions is sometimes called unified field theory. Such theories… … Universalium
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grand unified theory — noun Date: 1978 any of several theories that seek to unite in a single mathematical framework the electromagnetic and weak forces with the strong force or with the strong force and gravity called also grand unification theory … New Collegiate Dictionary
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grand unification theory — grand unified theory grand unified theory, grand unification theory grand unification theory . (Theoretical physics) Any of a class of physics theories that attempts to explain the electroweak forces, stong force, and gravitation within a single… … The Collaborative International Dictionary of English