Spontaneous Symmetry Breaking
The symmetry breaking of SO(10) is usually done with a combination of (( a 45H OR a 54H) AND ((a 16H AND a ) OR (a 126H AND a )) ).
Let's say we choose a 54H. When this Higgs field acquires a GUT scale VEV, we have a symmetry breaking to Z2 ⋊ /Z2, i.e. the Pati-Salam model with a Z2 left-right symmetry.
If we have a 45H instead, this Higgs field can acquire any VEV in a two dimensional subspace without breaking the standard model. Depending on the direction of this linear combination, we can break the symmetry to SU(5)×U(1), the Georgi-Glashow model with a U(1) (diag(1,1,1,1,1,-1,-1,-1,-1,-1)), flipped SU(5) (diag(1,1,1,-1,-1,-1,-1,-1,1,1)), SU(4)×SU(2)×U(1) (diag(0,0,0,1,1,0,0,0,-1,-1)), the minimal left-right model (diag(1,1,1,0,0,-1,-1,-1,0,0)) or SU(3)×SU(2)×U(1)×U(1) for any other nonzero VEV.
The choice diag(1,1,1,0,0,-1,-1,-1,0,0) is called the Dimopoulos-Wilczek mechanism aka the missing VEV mechanism and it is proportional to B−L.
The choice of a 16H and a breaks the gauge group down to the Georgi-Glashow SU(5). The same comment applies to the choice of a 126H and a .
It is the combination of BOTH a 45/54 and a 16/ or 126/ which breaks SO(10) down to the Standard Model.
Read more about this topic: SO(10) (physics)
Famous quotes containing the words spontaneous, symmetry and/or breaking:
“If an educational act is to be efficacious, it will be only that one which tends to help toward the complete unfolding of life. To be thus helpful it is necessary rigorously to avoid the arrest of spontaneous movements and the imposition of arbitrary tasks.”
—Maria Montessori (18701952)
“What makes a regiment of soldiers a more noble object of view than the same mass of mob? Their arms, their dresses, their banners, and the art and artificial symmetry of their position and movements.”
—George Gordon Noel Byron (17881824)
“Hence to fight and conquer in all your battles is not supreme excellence; supreme excellence consists in breaking the enemys resistance without fighting.”
—Sun Tzu (65th century B.C.)