Collapse of Exotic Textures: Models
These are the relevant facts about the models considered in this paper,
in which a global symmetry group G is spontaneously broken to a subgroup
H. "Fields" is the number of real scalar fields; the twelve real fields
in the SU(3) theory are arranged into two complex three-vectors, while
the other representations are explicitly real. The lower homotopy groups
of the vacuum manifold G/H are listed, as well as the dimensionality of
G/H (corresponding to the number of massless Goldstone bosons).
Note that one of the models, SO(5)/SO(4), has pi_3(G/H)=0; nevertheless,
a texture-like configuration can be constructed, even though it will
be topologically trivial.
Theory | Fields |
pi_1(G/H) | pi_2(G/H) |
pi_3(G/H) | dim(G/H) |
| SO(4) -> SO(3) | 4 |
0 | 0 | Z | 3 |
| SO(5) -> SO(4) | 5 |
0 | 0 | 0 | 4 |
| SO(5) -> SO(3) | 10 |
0 | 0 | Z_2 | 7 |
| SU(3) -> 0 | 12 |
0 | 0 | Z | 8 |
| SO(3) -> SO(2) | 3 |
0 | Z | Z | 2 |
| SO(3) -> 0 | 6 |
Z_2 | 0 | Z | 3 |
| SO(4) -> U(2) | 6 |
Z_2 | Z |
Z_2 | 2 |
| SO(5) -> SO(3)xSO(2)xZ_2 | 14 |
Z_2 | Z |
Z_2 | 6 |
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