Coupling unification

A Grand Unified Theory (GUT) is a model in particle physics in which, at high energies, the three gauge interactions of the Standard Model comprising the electromagnetic, weak, and strong forces are merged into a single force. Although this unified force has not been directly observed, many GUT models theorize its existence. If unification of these three interactions is possible, it raises the possibility that there was a grand unification epoch in the very early universe in which these three fundamental interactions were not yet distinct.

Experiments have confirmed that at high energy the electromagnetic interaction and weak interaction unify into a single electroweak interaction. GUT models predict that at even higher energy, the strong interaction and the electroweak interaction will unify into a single electronuclear interaction. This interaction is characterized by one larger gauge symmetry and thus several force carriers, but one unified coupling constant. Unifying gravity with the electronuclear interaction would provide a more comprehensive theory of everything (TOE) rather than a Grand Unified Theory. Thus, GUTs are often seen as an intermediate step towards a TOE.

The novel particles predicted by GUT models are expected to have extremely high masses—around the GUT scale of $10^$ GeV (just a few orders of magnitude below the Planck scale of $10^$ GeV)—and so are well beyond the reach of any foreseen particle hadron collider experiments. Therefore, the particles predicted by GUT models will be unable to be observed directly, and instead the 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. Some GUTs, such as the Pati–Salam model, predict the existence of magnetic monopoles.

While GUTs might be expected to offer simplicity over the complications present in the Standard Model, realistic models remain complicated because they need to introduce additional fields and interactions, or even additional dimensions of space, in order to reproduce observed fermion masses and mixing angles. This difficulty, in turn, may be related to an existence of family symmetries beyond the conventional GUT models. Due to this, and the lack of any observed effect of grand unification so far, there is no generally accepted GUT model.

Models that do not unify the three interactions using one simple 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.

History

Historically, the first true GUT which was based on the simple Lie group , was proposed by Howard Georgi and Sheldon Glashow in 1974. The Georgi–Glashow model was preceded by the semisimple Lie algebra Pati–Salam model by Abdus Salam and Jogesh Pati also in 1974, 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 they opted for the less anatomical GUM (Grand Unification Mass). Nanopoulos later that year was the first to use the acronym in a paper.

Motivation

The ''supposition'' 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 and which allow only discrete charges, the remaining component, the weak hypercharge interaction is described by an abelian symmetry which in principle allows for arbitrary charge assignments.There are however certain constraints on the choice of particle charges from theoretical consistency, in particular anomaly cancellation. The observed charge quantization, namely the postulation that all known elementary particles carry electric charges which are exact multiples of one-third 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 field theory of electromagnetism in the 19th century, but its physical implications and mathematical structure are qualitatively different.

Unification of matter particles

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

:$\rm SU(5) \supset SU(3)\times SU(2)\times U(1)$.

Such group symmetries allow the reinterpretation of several known particles, including the photon, W and Z bosons, and gluon, 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 matter particles fit perfectly into three copies of the smallest group representations of 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 are (the defining representation) and . In the standard assignment, the contains the charge conjugates of the right-handed down-type quark color triplet and a left-handed lepton isospin doublet