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:
“What is saved in the cinema when it achieves art is a spontaneous continuity with all mankind. It is not an art of the princes or the bourgeoisie. It is popular and vagrant. In the sky of the cinema people learn what they might have been and discover what belongs to them apart from their single lives.”
—John Berger (b. 1926)
“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 (1788–1824)
“The defects and faults of the mind are like wounds in the body; after all imaginable care has been taken to heal them up, still there will be a scar left behind, and they are in continual danger of breaking the skin and bursting out again.”
—François, Duc De La Rochefoucauld (1613–1680)