Grand Unified Theories

In General > s.a. symmetry breaking; types of yang-mills theories; unified theories.
* History: 1974, Idea proposed by Georgi and Glashow.
* Idea: Theories that unify the electroweak and strong interactions, usually described by a (Yang-Mills) gauge theory, where the interaction is mediated by a connection/potential belonging to (the Lie algebra of) a single group; Gravity is still not included in the unification.
* Structure: Like other gauge theories, they are based on a principal fiber bundle over spacetime (suitably compactified from boundary conditions), with a certain structure group G, and the quarks and leptons are described by a cross section of appropriate associated vector bundles; The interactions are mediated by connections, which are determined by the critical points of action integrals constructed as spacetime integrals of the curvature and its Hodge dual.
* Gauge group: Several groups have been proposed as strong candidates for grand unification, in particular SU(5), now known to be inadequate (1994); SO(10); Exceptional groups like E₆, which could come from the E₈ of string theory, E₇, and E₈.
* Symmetry breaking: All of the above are assumed to break to SU(3) × SU(2) × U(1) \(\mapsto\) SU(3) × U(1).
@ Introductions and reviews: Georgi & Glashow PT(80)sep; Georgi SA(81)apr; Langacker PRP(81); Baez & Huerta BAMS(10)-a0904 [for mathematicians]; Vafa a0911-conf [and geometry]; Croon et al FrPh(19)-a1903 [status].
@ Books: Cline & Mills ed-78; Zee 82; Ross 84; Kounnas et al 85.
@ Models, approaches: Georgi & Glashow PRL(74) [SU(5)]; Maraner MPLA(04)ht/03 [spacetime extensions of SO(10)]; Dorsner & Fileviez Pérez NPB(05)hp [non-supersymmetric SU(5)]; Edwards PLB(15)-a1411 [worldline approach]; Pauchy Hwang a1506 [SU_c(3) × SU_L(2) × U(1) × SU_f(3)]; Frezzotti et al PRD(16)-a1602 [non-supersymmetric model]; Britto a2102-MS [E₆].
> Online resources: Wikipedia page.

Phenomenology > s.a. inflation scenarios; neutrino; monopoles.
* Motivation: (i) Observed family structure; (ii) Meeting of the gauge couplings; (iii) Neutrino oscillations; (iv) The intricate pattern of masses and mixings of all fermions, including neutrinos; and (v) Need for B-L as a generator, to implement baryogenesis.
* Indications: 2000, Evidence favors grand unification along a particular route, based on the ideas of supersymmetry, SU(4)-color and left-right symmetry; This points to the relevance of an effective string-unified G(224) or SO(10)-symmetry.
* Successes: Prediction of sin²θ_W to within 5%; Elegant classification of particles.
* Problems: Quark/lepton mass ratios; Proton decay.
* Leptoquark: A hypothetical particle that turns quarks into leptons and vice versa, which arises naturally in GUTs; Depending on the model, they may form a singlet, a doublet, or a triplet (one particle may have charge +2/3, another −1/3); Their masses are estimated to be at least in the hundreds of GeV, possibly around a TeV; If they exist, they may offer an explanation for the NuTeV anomaly in neutrino physics, and the LHC will search for them.
@ Coupling constants: Bennet & Nielsen IJMPA(94).
@ Astrophysics and cosmology: Singh FdP(83); Dorsner et al NPB(06); Arvanitaki et al PRD(09)-a0812 + Pierce Phy(09).

Proton Decay > s.a. protons.
* Decay modes: The dominant one may be \(\bar\nu\,K^+\), with \(\mu^+ K^0\) being another possibility.
* Lifetime: (Maurice Goldhaber pointed out that if protons had a lifetime shorter than \(10^{17}\) years, you would "feel it in your bones".) In a typical (non-supersymmetric) version of GUT, the lifetime is predicted around 5 × 10²⁹ yr, while experimentally one gets \(\tau > 10^{30}\) yr and \(5 \times 10^{31} - 5 \times 10^{32}\) yr for neutrino and neutrinoless decays, respectively; A conservative estimate is about 1 × 10³⁴ yr.
* Status: From Superkamiokande, in 1998, τ ≥ 1.6 × 10³³ yr [@ Shiozawa et al PRL(98)]; in 2014, τ ≥ 5.9 × 10³³ yr [@ Abe et al PRD(14)]; in 2018, τ ≥ 1.6 × 10³⁴ yr [@ news econ(18)jan], which rules out simpler GUTs (including the SU(5) theory by Georgi and Glashow from 1974).
@ References: Goldhaber et al Sci(80)nov*; Weinberg SA(81)jun; Sulak AS(82); Pati AIP(00)hp; Dorsner & Fileviez Pérez PLB(05)hp/04 [upper bound on lifetime]; Frampton MPLA(07) [in teravolt unification].

Beyond Regular GUTs > s.a. action for general relativity; cosmic strings; kaluza-klein theory; particle physics.
* Supersymmetric GUTs: Adding supersymmetry gives an extended proton lifetime, among other benefits; > s.a. supersymmetric theories.
* Finite Unified Theories (FUTs): N = 1 supersymmetric Grand Unified Theories that can be made all-loop finite.
@ Supersymmetric GUTs: Sakellariadou & Rocher hp/04-proc, Rocher & Sakellariadou JCAP(05) [and cosmic strings]; Mondragón & Zoupanos Sigma(08)-a0802 [reduction of couplings]; Heinemeyer et al JHEP(08) [FUTs and phenomenology]; Arnowitt et al IJMPA(12)-a1206 [history, 1982-1985].
@ And gravity: Nesti & Percacci PRD(10)-a0909 [and chirality]; Calmet & Yang PRD(11)-a1105 [gravitational corrections to fermion masses].
@ And brane world: Duff IJMPA(01)ht/00-conf; Berenstein ht/06.
@ And strings: Pati IJMPD(06).
@ Quantum-gravity effects: Scardigli NPPS(00)ht/99 [scale]; Calmet et al PRL(08)-a0805, AIP(09)-a0809 [scale and possibility of unification].
@ Non-commutative: Aschieri et al NPB(03)ht/02; Calmet EPJC(07) [non-commutative spacetime]; Martin PoS-a1101 [rev].
@ Generalized: Froggatt et al NPB(94) [anti-grand unification, and fermion masses]; Spaans gq/97 [topological]; Chaves & Morales MPLA(00)ht/99 [with generalized Yang-Mills theory]; > s.a. symmetries [nilpotent].

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