Trinification
Encyclopedia
In physics
, the trinification model is a GUT
theory.
It states that the gauge group is either
or
;
and that the fermions form three families, each consisting of the representations :
, 
and :
.
This includes the right-handed neutrino, which can account for observed neutrino masses (but has not yet been proved to exist). See neutrino oscillation
s.
There is also a
and maybe also a 
scalar field
called the Higgs field which acquires a VEV. This results in a spontaneous symmetry breaking
from
to 
and also,
,
,
,
,
,
.
See restricted representation
.
Note that there are two Majorana neutrinos per generation (which is consistent with neutrino oscillation
s). Also, a copy of
and 
as well as
and 
per generation decouple at the GUT breaking scale due to the couplings
and
.
Note that calling the representations things like
and (8,1,1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableau
x or Dynkin diagrams with numbers on their vertices, but still, it is standard among GUT theorists.
Since the homotopy group
,
this model predicts monopoles. See 't Hooft-Polyakov monopole
.
This model is suggested by Sheldon Lee Glashow
, Howard Georgi
and Alvaro de Rujula, in 1984. This is one of the maximal subalgebra of E6, whose matter representation 27 has exactly the same representation as above.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, the trinification model is a GUT
Grand unification theory
The term Grand Unified Theory, often abbreviated as GUT, refers to any of several similar candidate models in particle physics in which at high-energy, the three gauge interactions of the Standard Model which define the electromagnetic, weak, and strong interactions, are merged into one single...
theory.
It states that the gauge group is either
or
;and that the fermions form three families, each consisting of the representations :
, and :.This includes the right-handed neutrino, which can account for observed neutrino masses (but has not yet been proved to exist). See neutrino oscillation
Neutrino oscillation
Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...
s.
There is also a
and maybe also a scalar fieldScalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...
called the Higgs field which acquires a VEV. This results in a spontaneous symmetry breaking
Spontaneous symmetry breaking
Spontaneous symmetry breaking is the process by which a system described in a theoretically symmetrical way ends up in an apparently asymmetric state....
from
to and also,
,,,,,.See restricted representation
Restricted representation
In mathematics, restriction is a fundamental construction in representation theory of groups. Restriction forms a representation of a subgroup from a representation of the whole group. Often the restricted representation is simpler to understand...
.
Note that there are two Majorana neutrinos per generation (which is consistent with neutrino oscillation
Neutrino oscillation
Neutrino oscillation is a quantum mechanical phenomenon predicted by Bruno Pontecorvowhereby a neutrino created with a specific lepton flavor can later be measured to have a different flavor. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates...
s). Also, a copy of
and as well as
and per generation decouple at the GUT breaking scale due to the couplings
and
.Note that calling the representations things like
and (8,1,1) is purely a physicist's convention, not a mathematician's convention, where representations are either labelled by Young tableauYoung tableau
In mathematics, a Young tableau is a combinatorial object useful in representation theory. It provides a convenient way to describe the group representations of the symmetric and general linear groups and to study their properties. Young tableaux were introduced by Alfred Young, a mathematician at...
x or Dynkin diagrams with numbers on their vertices, but still, it is standard among GUT theorists.
Since the homotopy group
Homotopy group
In mathematics, homotopy groups are used in algebraic topology to classify topological spaces. The first and simplest homotopy group is the fundamental group, which records information about loops in a space...
,this model predicts monopoles. See 't Hooft-Polyakov monopole
't Hooft-Polyakov monopole
In theoretical physics, the t Hooft–Polyakov monopole is a topological soliton similar to the Dirac monopole but without any singularities. It arises in the case of a Yang–Mills theory with a gauge group G, coupled to a Higgs field which spontaneously breaks it down to a smaller group H via the...
.
This model is suggested by Sheldon Lee Glashow
Sheldon Lee Glashow
Sheldon Lee Glashow is a Nobel Prize winning American theoretical physicist. He is the Metcalf Professor of Mathematics and Physics at Boston University.-Birth and education:...
, Howard Georgi
Howard Georgi
Howard Mason Georgi III, born January 6, 1947 in San Bernardino, California, is Harvard College Professor and Mallinckrodt Professor of Physics at Harvard University...
and Alvaro de Rujula, in 1984. This is one of the maximal subalgebra of E6, whose matter representation 27 has exactly the same representation as above.