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.

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.

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.

This model doesn't predict gauge mediated proton decay ( unless it is embedded within an even larger GUT group ).

Flipped SU ( 5 ) is not a fully unified model, because the U ( 1 ) y factor of the SM gauge group is within the U ( 1 ) factor of the GUT group.

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 equal in strength and unify to one force governed by a simple Lie group.

In particle physics, one of the grand unified theories ( GUT ) is based on the SO ( 10 ) Lie group.

To see this, note that with a 16 < sub > 1H </ sub > and a Higgs field, we can have VEVs which breaks the GUT group down to × U ( 1 )< sub > χ </ sub >/ Z < sub > 4 </ sub >.

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 < sup > 16 </ sup > GeV, which is slightly suggestive.

In this graph, electroweak unification occurs at around 100 GeV, grand unification is predicted to occur at 10 < sup > 16 </ sup > GeV, and unification of the GUT force with gravity is expected at the Planck energy, roughly 10 < sup > 19 </ sup > GeV.

Calling the representations foe example, and 24 < sub > 0 </ sub > is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, and is a standard used by GUT

When this Higgs field acquires a GUT scale VEV, we have a symmetry breaking to Z < sub > 2 </ sub > ⋊ × SU ( 2 )< sub > L </ sub > × SU ( 2 )< sub > R </ sub >/ Z < sub > 2 </ sub >, i. e. the Pati-Salam model with a Z < sub > 2 </ sub > left-right symmetry.

Image: Proton_decay2. svg | Dimension 6 proton decay mediated by the X boson in SU ( 5 ) GUT

Image: proton decay3. svg | Dimension 6 proton decay mediated by the X boson in flipped SU ( 5 ) GUT

Image: proton decay4. svg | Dimension 6 proton decay mediated by the triplet Higgs and the anti-triplet Higgs in SU ( 5 ) GUT

Of course, calling the representations things like and ( 6, 1, 1 ) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, but still, it is standard among GUT theorists.

Dimension 6 proton decay mediated by the boson in flipped GUT

Dimension 6 proton decay mediated by the triplet Higgs and the anti-triplet Higgs in GUT

Since Majorana masses of the right-handed neutrino are forbidden by SO ( 10 ) symmetry, SO ( 10 ) GUTs predict the Majorana masses of right-handed neutrinos to be close to the GUT scale where the symmetry is spontaneously broken in those models.

A number of other GUT models are based upon subgroups of SO ( 10 ).

Some GUT theories like SU ( 5 ) and SO ( 10 ) suffer from what is called the doublet-triplet problem.

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 ).

Schematic representation of fermions and bosons in SU ( 5 ) GUT showing 5 + 10 split in the multiplets.

If the hypercharge is contained within SU ( 5 ), this is the conventional Georgi-Glashow model, with the 16 as the matter fields, the 10 as the electroweak Higgs field and the 24 within the 45 as the GUT Higgs field.

A Grand Unified Theory, ( GUT ), is a model in particle physics in which at high energy, 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.

Unifying gravity with the other three interactions would provide a theory of everything ( TOE ), rather than a GUT.

* GUT ( band ), a German goregrind band

In these classes of models collectively now known as minimal supergravity Grand Unification Theories ( mSUGRA GUT ), gravity mediates the breaking of SUSY through the existence of a hidden sector.

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 so-called 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.

, 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.

Some common mainstream GUT models are:

GUT models generically predict the existence of topological defects such as monopoles, cosmic strings, domain walls, and others.

Most GUT models also predict proton decay, although not the Pati-Salam model ; current experiments still haven't detected proton decay.

Most GUT models require a threefold replication of the matter fields.

Most GUT models also fail to explain the little hierarchy between the fermion masses for different generations.

New models of GUT unification of the fundamental forces have recently been developed using F-theory.

He ignored magnetic monopoles because they were based on assumptions of GUT, which was outside the scope of the speech.

There are a few more special tests for supersymmetric GUT.

Note that calling the representations things like and ( 8, 1, 1 ) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableaux or Dynkin diagrams with numbers on their vertices, but still, it is standard among GUT theorists.

Since monopoles are generically produced in GUT during the cooling of the universe, and since they are expected to be quite massive, their existence threatens to overclose it.

The primary problem with these color triplet Higgs, is that they can mediate proton decay in supersymmetric theories that are only suppressed by two powers of GUT scale ( i. e. they are dimension 5 supersymmetric operators ).

At GUT scale, these are sometimes quoted as: