physics, mathematical physics, philosophy of physics
theory (physics), model (physics)
experiment, measurement, computable physics
Axiomatizations
Tools
Structural phenomena
Types of quantum field thories
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 $G$-principal bundle, where the Lie group $G$ – called the gauge group – is the product of (special) unitary groups $G = SU(3) \times SU(2) \times U(1)$ (or rather a quotient of this by the cyclic group $Z/6$) and where the representation of $G$ 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 $\hat{G}$, preferably a simple Lie group in the technical sense, which contains $G$ 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 $\hat{G}$ 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 force and electromagnetism, and electromagnetism already unifies, as the word says, electricity and magnetism.
Historically, the most studied choices of GUT-groups $G$ 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).
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.)
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.
Recently it was claimed that there are in fact realistic GUT models that do not imply any proton decay (Mütter-Ratz-Vaudrvange 16, Fornal-Grinstein 17).
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).
An original article with an eye towards supergravity unification is
Survey of arguments for the hypothesis of grand unification includes
Michael Peskin, Beyond the Standard Model (arXiv:hep-ph/9705479)
Jogesh Pati, Discovery of Proton Decay: A Must for Theory, a Challenge for Experiment (arXiv:hep-ph/0005095)
Edward Witten, Quest For Unification, Heinrich Hertz lecture at SUSY 2002 at DESY, Hamburg (arXiv:hep-ph/0207124)
Introduction to GUTs aimed more at mathematicians include
Edward Witten, section 1 and 2 of Physics and geometry, Proceedings of the international congress of mathematicians, 1986 (pdf)
John Baez, John Huerta, The Algebra of Grand Unified Theories, Bull.Am.Math.Soc.47:483-552,2010 (arXiv:0904.1556)
Discussion of comparison of GUTs to experiment and phenomenology includes
for non-superymmetric models:
Guido Altarelli, Davide Meloni, A non Supersymmetric SO(10) Grand Unified Model for All the Physics below $M_{GUT}$ (arXiv:1305.1001)
Alexander Dueck, Werner Rodejohann, Fits to $SO(10)$ Grand Unified Models (arXiv:1306.4468)
Chee Sheng Fong, Davide Meloni, Aurora Meroni, Enrico Nardi, Leptogenesis in $SO(10)$ (arXiv:1412.4776)
for supersymmetric models:
Archana Anandakrishnan, B. Charles Bryant, Stuart Raby, LHC Phenomenology of $SO(10)$ Models with Yukawa Unification II (arXiv:1404.5628)
Ila Garg, New minimal supersymmetric $SO(10)$ GUT phenomenology and its cosmological implications (arXiv:1506.05204)
Realization of GUTs in the context of M-theory on G2-manifolds and possible resolution of the doublet-triplet splitting problem is discussed in
Edward Witten, Deconstruction, $G_2$ Holonomy, and Doublet-Triplet Splitting, (arXiv:hep-ph/0201018)
Bobby Acharya, Krzysztof Bozek, Miguel Crispim Romao, Stephen F. King, Chakrit Pongkitivanichkul, $SO(10)$ Grand Unification in M theory on a $G_2$ manifold (arXiv:1502.01727)
Discussion of GUTs in F-theory includes
Chris Beasley, Jonathan Heckman, Cumrun Vafa, GUTs and Exceptional Branes in F-theory - I (arxiv:0802.3391), II: Experimental Predictions (arxiv:0806.0102)
Chris Beasley, Jonathan Heckman, Cumrun Vafa, GUTs and Exceptional Branes in F-theory - I, JHEP 0901:058,2009 (arXiv:0802.3391)
Gianluca Zoccarato, Yukawa couplings at the point of $E_8$ in F-theory, 2014 (pdf/zoccarato.pdf))
Cumrun Vafa, Reflections on F-theory, 2015 (pdf)
Discussion of experimental bounds on proton decay in GUTs includes
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, $SU(5)$ Unification without Proton Decay, Physics Review Letters (arXiv:1706.08535)