Last Update 2018/01/25
In the 1960’s, scientists discovered that the variety in the types of light mesons and their interactions derives from an underlying symmetry and its spontaneous breaking. Applying this idea to the variety in the types of elementary particles in the Standard Model and their Yukawa interactions, my collaborator and I pointed out in 2006 that an En type Lie algebra and its symmetry breaking may be at work behind the Standard Model.
In string theory compactification, the algebra arises from topology of a geometry. In order to know more about the detailed pattern of Yukawa couplings, however, non-topological aspects of the geometry are also involved. Neutrino oscillation experiments have revealed that the leptons have large mixing angles, which contrasts sharply with small-angle quark mixing. This contrast has been the biggest theoretical puzzle associated with the Yukawa couplings. Can this puzzle be solved in terms of geometry? I am looking for the answer to that and other questions.
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