Grand unification theory

A Grand Unification Theory (TGU, in English, Grand Unification Theory, GUT) is a theory which would unify three of the four fundamental forces in nature: the weak nuclear force, the strong nuclear force, and the electromagnetic force. The force of gravity is not considered in this theory, but it is in a possible theory of everything (Theory of Everything, ToE), which would consider the four fundamental interactions.

Steven Weinberg and Abdus Salam elaborated in 1967-1968, a relativistic theory of the quantum field, which allowed to express the electromagnetic and weak interactions in a unified way (electroweak model), and which predicted facts that were later verified experimentally. Subsequently, Howard Georgi and Sheldon Lee Glashow developed a new theory, which added new features and corrected some errors and omissions from the previous theory. However, the decay of the proton emerged from the equations. This led to some famous experiments to detect this effect: but since the lifetime of a proton is very long, on the order of 10³¹ years, it is not possible to observe the particle long enough to witness the decomposition. In lieu of this, perhaps the effect could be observed if enough protons are examined. Some known measurement attempts were made in large underground pools (to protect the experiment from radiation), in which the decay of the proton would be visualized as a flash in a series of photosensors.

Mathematical formulation

The standard model of particle physics is a gauge field theory that describes elementary fermions (leptons and quarks) interacting with each other through a series of intermediary boson Yang-Mills fields. Since the electroweak model (which describes the electromagnetic and weak interaction) is based on a gauge theory with gauge group of symmetry SU(2)xU(1) and quantum chromodynamics (which describes the strong interaction) is based on a theory with gauge group SU(3); Physicists have found it promising to describe all these interactions by a gauge theory with a symmetry group having the aforementioned gauge groups as subgroups.

SU(5)

An obvious candidate for a symmetry group is SU(5) on which the 1974 Georgi-Glashow model is based. In that model a spontaneous symmetry breaking mechanism was included whereby the original symmetry is complete, it became a less general symmetry U(1)xSU(2)xSU(3) at low energies by symmetry-breaking phenomena. Although at high energies the rupture factors become irrelevant and the three types of interaction should appear as manifestations of the same field. One of the predictions of this model is that there would be interactions that would transform quarks into leptons violating the conservation of baryon number (although the sum of the baryon number plus the lepton number would still be conserved). One of those aforementioned interactions would allow the disintegration of the proton into other lepton particles. Since the theory itself allows the decay rate to be calculated, in principle it is more or less straightforward to test the theory. Unfortunately, the disintegration of the proton has not been observed and the experimental error limits allow us to rule out the theory, which is why other gauge symmetry groups have been sought that lead to predictions in agreement with what has been observed. Although the elegance of this theory has made it the basis of many other later proposals somewhat more complicated.

Other proposals

Many grand unification theories with gauge group having as subgroups the gauge group of the Standard Model (U(1)xSU(2)xSU(3)) have been proposed, although none of them are generally accepted. Some conventional grand unified theories are:

• Levogiro-dextrogy model based on SU(3)C× × SU(2)L× × SU(2)R× × U(1)B− − L{displaystyle scriptstyle SU(3)_{C}times SU(2)_{L}times SU(2)_{R}times U(1)_{B-L}}}}
• Georgi-Fritzsch-Minkowski model, based on SO(10){displaystyle scriptstyle SO(10)}
• Modified SU(5) model, based on SU(5)× × U(1)χ χ ]/Z5{displaystyle scriptstyle SU(5)times U(1)_{chi }]/mathbb {Z} _{5}
• Modified SO(10) model SO(10)× × U(1){displaystyle scriptstyle SO(10)times U(1)}
• Pati-Salam Model SU(4)× × SU(2)× × SU(2){displaystyle scriptstyle SU(4)times SU(2)times SU(2)} (o) SU(4)× × SU(2)L× × SU(2)R{displaystyle scriptstyle SU(4)times SU(2)_{L}times SU(2)_{R}}})
• Cyral model, based on SU(3)R× × SU(3)L{displaystyle scriptstyle SU(3)_{R}times SU(3)_{L}}}
• Trinification model, based on SU(3)× × SU(3)× × SU(3){displaystyle scriptstyle SU(3)times SU(3)times SU(3)} (o) SU(3)C× × SU(3)L× × SU(3)R{displaystyle scriptstyle SU(3)_{C}times SU(3)_{L}times SU(3)_{R})
• Ernest Ma model, based on SU(3)q× × SU(3)L× × SU(2)× × SU(2)× × U(1){displaystyle scriptstyle SU(3)_{q}times SU(3)_{L}times SU(2)times SU(2)times U(1)}
• Ernest Ma model, based on SU(3)4× × SU(3)6{displaystyle scriptstyle SU(3)^{4}times SU(3)^{6}}}
• Model SU(6), based on SU(6){displaystyle scriptstyle SU(6)}
• Model SU(6)⁴ x Z₄based on SU(6)4× × Z4{displaystyle scriptstyle SU(6)^{4}times Z_{4}}}
• Model SU(8), based on SU(8){displaystyle scriptstyle SU(8)}
• Model O(16), based on O(16){displaystyle scriptstyle O(16)}
• Model AMOSA13(13), based on AMOSA13(13){displaystyle scriptstyle AMOSA13(13)}
• Model E₆based on E6{displaystyle scriptstyle E_{6}}
• Model E₈based on E8{displaystyle scriptstyle E_{8}}