Back to Algebraic Geometry Seminar: Fall 2014
Algebraic Geometry Seminar
Date: Tuesday, Sep 23, 2014
Time: 3:30PM - 4:30PM
Location: LCB 225
Herbert Clemens
University of Utah
Title |
A global model for heterotic - F-theory duality with Wilson line symmetry breaking |
Abstract |
We construct a global geometric model for heterotic - F-theory duality, that is, a Calabi-Yau threefold with two flat E_8 bundles with SU(5)-symmetry (heterotic side) and a Calabi-Yau fourfold with SU(5) root symmetry (F-theory side), both equipped with compatible involutions that, in the respective quotients, break the SU(5)-symmetry to the SU(3)xSU(2)xU(1)-symmetry of the physics ‘standard model.’ The duality is realized by an equivariant semi-stable degeneration of the Calabi-Yau fourfold to the union of two components, each of which is a so-called DP9-bundle containing a common Calabi-Yau threefold (along which the two components are joined). A result of Friedman-Morgan-Witten, gives a dictionary between flat E_8 bundles and DP9-bundles. (NB: The terminology DP9 stands for ‘Del Pezzo 9-surface’ which the string theorists use for something that is, in fact, not a Del Pezzo surface but what you get when you blow up the one-point base locus of |-K| in a Del Pezzo surface with (-K)^2 = 1.) This is joint with S. Raby and T. Pantev. |
Algebraic Geometry