General idea

The standard model of particle physics asserts that the fundamental quantum physical fields and particles are modeled as sections of and connections on a vector bundle that is associated to a GG-principal bundle, where the Lie group GG – called the gauge group – is the product of (special) unitary groups G=SU(3)×SU(2)×U(1)G = SU(3) \times SU(2) \times U(1) (or rather a quotient of this by the cyclic group Z/6Z/6, see there) and where the representation of GG used to form the associated vector bundle looks fairly ad hoc on first sight.

A grand unified theory (“GUT” for short) in this context is an attempt to realize the standard model as sitting inside a conceptually simpler model, in particular one for which the gauge group is a bigger but simpler group G^\hat{G}, preferably a simple Lie group in the technical sense, which contains GG as a subgroup. Such a grand unified theory would be phenomenologically viable if a process of spontaneous symmetry breaking at some high energy scale – the “GUT scale” – would reduce the model back to the standard model of particle physics without adding spurious extra effects that would not be in agreement with existing observations in experiment.

The terminology “grand unified” here refers to the fact that such a single simple group G^\hat{G} would unify the fundamental forces of electromagnetism, the weak nuclear force and the strong nuclear force in a way that generalizes the way in which the electroweak field already unifies the weak nuclear force and electromagnetism, and electromagnetism already unifies, as the word says, electricity and magnetism.

Since no GUT model has been fully validated yet (but see for instance Fong-Meloni 14), GUTs are models “beyond the standard model”. Often quantum physics “beyond the standard model” is expected to also say something sensible about quantum gravity and hence unify not just the three gauge forces but also the fourth known fundamental force, which is gravity. Models that aim to do all of this would then “unify” the entire content of the standard model of particle physics plus the standard model of cosmology, hence “everything that is known about fundamental physics” to date. Therefore such theories are then sometimes called a theory of everything.

(Here it is important to remember the context, both “grand unified” and “of everything” refers to aspects of presently available models of fundamental physics, and not to deeper philosophical questions of ontology.)

The SU(5)SU(5)-GUT (Georgi-Glashow)

The argument for the hypothesis of “grand unification” is fairly compelling if one asks for simple algebraic structures in the technical sense (simple Lie groups and their irreducible representations):

The exact gauge group of the standard model of particle physics is really a quotient group

G SM=(U(1)×SU(2)×SU(3))/ 6, G_{SM} \;=\; \big( U(1) \times SU(2) \times SU(3) \big) / \mathbb{Z}_6 \,,

where the cyclic group 6\mathbb{Z}_6 acts freely, hence exhibiting a subtle global twist in the gauge structure. This seemingly ad hoc group turns out to be isomorphic to the subgroup

S(U(2)×U(3))(U(1)×SU(2)×SU(3))/ 6SU(5) \underset{ \simeq \big( U(1) \times SU(2) \times SU(3) \big) / \mathbb{Z}_6 }{ \underbrace{ S \big( U(2) \times U(3)\big) }} \;\subset\; SU(5)

of SU(5) (see Baez-Huerta 09, p. 33-36). The latter happens to be a simple Lie group, thus exhibiting the exact standard model Lie group as being “simply” a “(2+3)-breaking” of a simple Lie group.

Moreover, the gauge group-representation V SMV_{SM} that captures one generation of fundamental particles of the standard model of particle physics, which looks fairly ad hoc as a representation of G SMG_{SM} (e.g. Baez-Huerta 09, table 1), but as a representation of SU(5)SU(5) it is simply

V SMΛ 5 V_{SM} \simeq \Lambda \mathbb{C}^5

(see Baez-Huerta 09, p. 36-41).

This leads to the SU(5)SU(5)-GUT due to Georgi-Glashow 74

The Spin(10)Spin(10)-GUT (known as “SO(10)SO(10)”)

There is a further inclusion SU(5)Spin(10)SU(5) \hookrightarrow Spin(10) into the spin group in 10 (Euclidean) dimensions (still a simple Lie group), and one generation of fundamental particles regarded as an SU(5)SU(5)-representation Λ 5\Lambda \mathbb{C}^5 as above extends to a spin representation (see Baez-Huerta 09, theorem 2). This has the aesthetically pleasing effect that under this identification the 1-generation rep V SMV_{SM} is now identified as

V SM1616¯ V_{SM} \;\simeq\; \mathbf{16} \oplus \overline{\mathbf{16}}

namely as the direct sum of the two (complex) irreducible representations of Spin(10)Spin(10), together being the Dirac representation of Spin(10)Spin(10).

Again, this means that under the embedding of the gauge group G SMG_{SM} all the way into the simple Lie group Spin(10)Spin(10), its ingredients become simpler, not just in a naive sense, but in the technical mathematical sense of simple algebraic objects.

Discussion of SO(10)SO(10) (i.e. Spin(10)Spin(10)) GUT-models with realistic phenomenology is in BLM 09 Malinský 09, Lavoura-Wolfenstein 10 Altarelli-Meloni 13 Dueck-Rodejohann 13 Ohlsson-Pernow 19 CPS 19.

slide grabbed from Malinský 09

Discussion of leptoquarks in SO(10)SO(10)-models possibly explaining the flavour anomalies: AMM 19

Exceptional series GUTs

This way, the most studied choices of GUT-groups GG are SU(5), Spin(10) (in the physics literature often referred to as SO(10)) and E6 (review includes Witten 86, sections 1 and 2).

It so happens that, mathematically, the sequence SU(5), Spin(10), E6 naturally continues (each step by consecutively adding a node to the Dynkin diagrams) with the exceptional Lie groups E7, E8 that naturally appear in heterotic string phenomenology (exposition is in Witten 02a) and conjecturally further via the U-duality Kac-Moody groups E9, E10, E11 that are being argued to underly M-theory. In the context of F-theory model building, also properties of the observes Yukawa couplings may point to exceptional GUT groups (Zoccarato 14, slide 11, Vafa 15, slide 11).


Relation to proton decay

Many GUT models imply that the proton – which in the standard model of particle physics is a stable bound state (of quarks) – is in fact unstable, albeit with an extremely long mean liftetime, and hence may decay (e.g. KM 14). Experimental searches for such proton decay (see there for more) put strong bounds on this effect and hence heavily constrain or rule out many GUT models.

But in recent years it is claimed that there are in fact realistic SU(5)SU(5) GUT models that do not imply any proton decay, quite generically so for MSSM-models (Mütter-Ratz-Vaudrvange 16), but also for a non-supersymmetric model (Fornal-Grinstein 17, Fornal-Grinstein 18).

Relation to neutrino masses

The high energy scale required by a seesaw mechanism to produce the experimentally observer neutrino masses happens to be about the conventional GUT scale, for review see for instance (Mohapatra 06).

I also noted at the same time that interactions between a pair of lepton doublets and a pair of scalar doublets can generate a neutrino mass, which is suppressed only by a factor M 1M^{-1}, and that therefore with a reasonable estimate of MM could produce observable neutrino oscillations. The subsequent confirmation of neutrino oscillations lends support to the view of the Standard Model as an effective field theory, with M somewhere in the neighborhood of 10 16GeV10^{16} GeV. (Weinberg 09, p. 15)

Detailed matching of parameters of non-supersymmetric Spin(10)Spin(10)-GUT to neutrino masses is discussed in Ohlsson-Pernow 19

Relation to leptoquarks

Generically, GUT-theories predict the existence of leptoquarks (Murayama-Yanagida 92), possibly related to the apparently observed

Occurrence in string phenomenology

Discussion of string phenomenology of intersecting D-brane models KK-compactified with non-geometric fibers such that the would-be string sigma-models with these target spaces are in fact Gepner models (in the sense of Spectral Standard Model and String Compactifications) is in (Dijkstra-Huiszoon-Schellekens 04a, Dijkstra-Huiszoon-Schellekens 04b):

A plot of standard model-like coupling constants in a computer scan of Gepner model-KK-compactification of intersecting D-brane models according to Dijkstra-Huiszoon-Schellekens 04b.

The blue dot indicates the couplings in SU(5)SU(5)-GUT theory. The faint lines are NOT drawn by hand, but reflect increased density of Gepner models as seen by the computer scan.



Original articles include

See also

An original article with an eye towards supergravity unification is

A basic textbook account is in

and a detailed one is in

Survey of arguments for the hypothesis of grand unification includes

Introduction to GUTs aimed more at mathematicians include

Proton (non-)decay

Discussion of experimental bounds on proton decay in GUTs includes

  • Helena Kolešová, Michal Malinský, Proton lifetime in the minimal SO(10)SO(10) GUT and its implications for the LHC, Phys. Rev. D 90, 115001 (2014) (arXiv:1409.4961)

Claim that proton decay may be entirely avoided:

  • Andreas Mütter, Michael Ratz, Patrick K.S. Vaudrevange, Grand Unification without Proton Decay (arXiv:1606.02303)

    (claims that many string theory and supergravity models have this property)

  • Bartosz Fornal, Benjamin Grinstein, SU(5)SU(5) Unification without Proton Decay, Physics Review Letters (arXiv:1706.08535)

  • Bartosz Fornal, Benjamin Grinstein, Grand Unified Theory with a Stable Proton, Int. J. Mod. Phys. A 33 (2018) 1844013 (arXiv:1808.00953)

Claim that threshold corrections can considerably alter (decrease) proton decay rate predictions in non-supersymmetric GUTs:

  • Joydeep Chakrabortty, Stephen F. King, Rinku Maji, Unification, Proton Decay and Topological Defects in non-SUSY GUTs with Thresholds (arXiv:1901.05867)

Realistic models and phenomenology

Discussion of phenomenologically viable GUT-models (compatible with experiment and the standard model of particle physics):

  • Stefano Bertolini, Luca Di Luzio, Michal Malinský, Intermediate mass scales in the non-supersymmetric SO(10) grand unification: a reappraisal, Phys. Rev. D80:015013, 2009 (arXiv:0903.4049)


for non-superymmetric models:

  • L. Lavoura and Lincoln Wolfenstein, Resuscitation of minimal SO(10)SO(10) grand unification, Phys. Rev. D 48, 264 (doi:10.1103/PhysRevD.48.264)

  • Guido Altarelli, Davide Meloni, A non Supersymmetric SO(10) Grand Unified Model for All the Physics below M GUTM_{GUT} (arXiv:1305.1001)

  • Alexander Dueck, Werner Rodejohann, Fits to SO(10)SO(10) Grand Unified Models (arXiv:1306.4468)

  • Chee Sheng Fong, Davide Meloni, Aurora Meroni, Enrico Nardi, Leptogenesis in SO(10)SO(10) (arXiv:1412.4776)

  • Tommy Ohlsson, Marcus Pernow, Fits to Non-Supersymmetric SO(10) Models with Type I and II Seesaw Mechanisms Using Renormalization Group Evolution (arXiv:1903.08241)

  • Mainak Chakraborty, M.K. Parida, Biswonath Sahoo, Triplet Leptogenesis, Type-II Seesaw Dominance, Intrinsic Dark Matter, Vacuum Stability and Proton Decay in Minimal SO(10) Breakings (arXiv:1906.05601)

    Results indicating non-SUSY SO(10)SO(10) as self sufficient theory for neutrino masses, baryon asymmetry, dark matter, vacuum stability of SM scalar potential, origin of three gauge forces, and observed proton stability.

  • Nobuchika Okada, Digesh Raut, Qaisar Shafi, Inflation, Proton Decay, and Higgs-Portal Dark Matter in SO(10)×U(1) priSO(10) \times U(1)_\pri (arXiv:1906.06869)

for supersymmetric models:

  • Archana Anandakrishnan, B. Charles Bryant, Stuart Raby, LHC Phenomenology of SO(10)SO(10) Models with Yukawa Unification II (arXiv:1404.5628)

  • Ila Garg, New minimal supersymmetric SO(10)SO(10) GUT phenomenology and its cosmological implications (arXiv:1506.05204)

In string theory

Introductory overview to GUTs in string theory is in

Amplifcation that SO(32)SO(32)-GUT (as in heterotic string theory and type I string theory) is viable via special subgroup-breaking:

Computer scan of Gepner model-compactifications in relation to GUT-models is in

Realization of GUTs in the context of M-theory on G2-manifolds and possible resolution of the doublet-triplet splitting problem is discussed in

Discussion of GUTs in F-theory includes

In Connes-Lott models

Discussion of GUTs within Connes-Lott models:

Exotica: Leptoquarks, ZZ'-bosons, etc.

Topological defects can play considerable role to constrain the non-SUSY and SUSY GUTs:

  • Joydeep Chakrabortty, Rinku Maji, Sunando Kumar Patra, Tripurari Srivastava, Subhendra Mohanty, Roadmap of left-right models based on GUTs (arXiv:1711.11391, Phys.Rev. D97 (2018) no.9, 095010.)

Relation to Z'-bosons:

  • S. Sahoo, The prediction of mass of ZZ'-boson in an SO(10)SO(10)-based model, Indian J. Phys. 80 (2), 191-194 (2006) (pdf)

Relation to leptoquarks and flavour anomalies:

  • H. Murayama, T. Yanagida, A viable SU(5)SU(5) GUT with light leptoquark bosons, Mod.Phys.Lett. A7 (1992) 147-152 (arXiv:315898, doi:10.1142/S0217732392000070)

  • Damir Bečirević, Ilja Doršner, Svjetlana Fajfer, Nejc Košnik, Darius A. Faroughy, Olcyr Sumensari, Scalar leptoquarks from GUT to accommodate the BB-physics anomalies, Phys. Rev. D 98, 055003 (2018) (arXiv:1806.05689)

  • Ufuk Aydemir, Tanumoy Mandal, Subhadip Mitra, A single TeV-scale scalar leptoquark in SO(10) grand unification and B-decay anomalies (arXiv:1902.08108)

  • Julian Heeck, Daniele Teresi, Pati-Salam explanations of the B-meson anomalies, JHEP 12 (2018) 103 (arXiv:1808.07492)

  • Julian Heeck, Daniele Teresi, Pati-Salam and lepton universality in B decays (arXiv:1905.05211)

  • Michal Malinský, Lepton non-universality in BB-decays in the minimal leptoquark gauge model (arXiv:1906.09174)

Last revised on June 24, 2019 at 03:22:49. See the history of this page for a list of all contributions to it.