Grand Unified Theory

For the album, see [[:Grand Unification (album)]].

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 $10^{14}$ GeV), the electromagnetic, weak nuclear, and strong nuclear forces are fused into a single unified field.

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.

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).

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 ($10\oplus {\bar {5}}$) 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.

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.

(For a more elementary introduction to how Lie algebras are related to particle physics, see the article Particle physics and representation theory.)

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.

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 left-right model -- $SU(3)_{C}\times SU(2)_{L}\times SU(2)_{R}\times U(1)_{B-L}$
• Georgi-Glashow model -- $SU(5)$
• SO(10)
• Flipped SU(5) -- $SU(5)\times U(1)$
• Pati-Salam model -- $SU(4)\times SU(2)\times SU(2)$
• flipped SO(10) -- $SO(10)\times U(1)$
• Trinification -- $SU(3)\times SU(3)\times SU(3)$
• SU(6)
• E₆
• 331 model
• chiral color
• Heim Theory

Not quite GUTs...

• Technicolor models
• Little Higgs
• Preons
• String theory
• M-theory
• Loop quantum gravity
• Causal Dynamical Triangulation Theory

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.

The most promising candidate is SO(10). (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.

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.

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).

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.

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. Moreover, since the Higgs particle has not yet been observed, the smaller electroweak unification is still pending. The discovery of neutrino oscillations indicate 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.

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 Pati-Salam group.

See also

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

References

• An account of the origin of the term GUT