Standard Model Group Research Articles

Standard model group: Survival of the fittest

The essential content of this paper is related to random dynamics. We speculate that the world seen through a sub-Planck-scale microscope has a lattice structure and that the dynamics on this lattice is almost completely random, except for the requirement that the random (plaquette) action is invariant under some “world (gauge) group”. We see that the randomness may lead to spontaneous symmetry breakdown in the vacuum (spontaneous collapse) without explicit appeal to any scalar field associated with the usual Higgs mechanism. We further argue that the subgroup which survives as the end product of a possible chain of collapses is likely to have certain properties; the most important is that it has a topologically connected center. The standard group, i.e. the group of the gauge theory which combines the Salam-Weinberg model with QCD, has this property.

Standard-model bundles

We describe a family of genus one fibered Calabi-Yau threefolds with fundamental group Z/2. On each Calabi-Yau Z in the family we exhibit a positive dimensional family of Mumford stable bundles whose symmetry group is the Standard Model group SU(3) × SU(2) × U(1) and which have c3 = 6. We also show that for each bundle V in our family, c2(Z) − c2(V ) is the class of an effective curve on Z. These conditions ensure that Z and V can be used for a phenomenologically relevant compactification of Heterotic M-theory. MSC 2000: 14D21, 14J32