Grand unification theory

Grand unification, grand unified theory, or GUT is a theory in physics that unifies the strong interaction and electroweak interaction.

Contents

1 Motivation 2 Proposed theories 3 Current status 4 See also

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 19^th century unification of electricity with magnetism and especially the success of the electroweak theory which utilizes the idea of spontaneously broken symmetry to unify electromagnetism with the weak interaction, people wondered if perhaps all the three groups might be unified in a similar manner. With three independent gauge coupling constants and a huge number of Yukawa coupling coefficients, physicists feel this is way 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. A problem is, though, that a GUT theory generically predicts relations among the fermion masses (e.g. between the electron and the down quark, the muon and the strange quark, and the tauon and the bottom quark for SU(5) and SO(10)) Some of these mass relations hold approximately, but unfortunately, most don't. If we look at the renormalization group running of the three gauge couplings, we find they nearly meet at the same point but not quite. However, if instead of using the Standard Model, we use its supersymmetric extension MSSM instead, the match becomes much more accurate. The common belief is this matching is unlikely to be a coincidence.

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:

• Left-right models
• Georgi-Glashow model -- SU(5)
• SO(10)
• Flipped SU(5) -- SU(5)×U(1)
• Pati-Salam model -- SU(4)×SU(2)×SU(2)
• Trinification -- SU(3)×SU(3)×SU(3)
• E₆
• Technicolor models
• String theory
• M-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.

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.

Current status

As of 2004, there is still no hard evidence nature is described by a GUT theory. In fact, since the Higgs particle hasn't been discovered yet, it is not even certain if the Standard Model is fully accurate.

GUT theories are based on the idea of a "desert" with no new physics of several orders of magnitude in the renormalization group. In that case, the gauge coupling strength of QCD, the weak interaction and hypercharge seem to meet at a common length scale called the GUT scale and equal approximately to <math>10^{16}<math> 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. The gauge coupling unification becomes physically irrelevant if the idea of the desert is incorrect.

See also

• Grand unification energybr:Peurunvanidigezh

ca:Teoria de la gran unificació de:Große vereinheitlichte Theorie fr:Grande unification ja:大統一理論 pl:Teorie wielkiej unifikacji sk:Teória veľkého zjednotenia sl:Teorija velikega poenotenja sv:Grand unification theory vi:Thuyết thống nhất zh:大统一理论