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 E_{6},
which could come from the E_{8} of string theory,
E_{7}, and E_{8}.

* __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 SA(81)apr;
Langacker PRP(81);
Baez & Huerta BAMS(10)-a0904 [for mathematicians];
Vafa a0911-conf [and geometry].

@ __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 a1602 [non-supersymmetric model].

> __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
sin^{2}*θ*_{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; 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 *ν*-bar *K*^{+}, with
*μ*^{+}*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 × 10^{29} yr,
while experimentally one gets *τ* > 10^{30} yr
and 5 × 10^{31}–5 × 10^{32} yr
for neutrino and neutrinoless decays, respectively; A conservative estimate
is about 1 × 10^{34} yr.

* __Status__: From Superkamiokande, in 1998,
*τ* ≥ 1.6 × 10^{33} yr [@ Shiozawa et al
PRL(98)]; in 2014,
*τ* ≥ 5.9 × 10^{33} yr [@ Abe et al
PRD(14)];
in 2018, *τ* ≥ 1.6 × 10^{34} 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].

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