Geometry, Topology, and Physics Seminar: Andreas Malmendier (Colby College), 'K3 surfaces from Seiberg-Witten curves'

Event Date: 

Friday, October 4, 2013 -
4:00pm to 5:30pm

Event Location: 

  • 6635 South Hall

Sen gave a description of the compactification of F-theory on a K3 surface in the orbifold limit where the surface appears as an orbifold of a four-torus. The corresponding picture in M-theory is a self-dual string from an intersecting M2 and M5-brane, and such a configuration corresponds to the lift of Seiberg-Witten theory to M-theory. This picture also provides an embedding of Seiberg-Witten theory into F-theory, by identifying the gauge coupling of gauge theory with the axion-dilaton modulus of string theory.

In my talk I will generalize Sen's procedure by constructing all 2-parameter families of lattice-polarized K3 surfaces that can be obtained from extremal rational elliptic surfaces through a quadratic twist. I will show that for all of these families the Picard-Fuchs system governing the K3-periods are obtained by an integral transform of a differential equation of hypergeometric or Heun type, and that in fact the K3-periods have an interpretation as modular forms. If time permits I will also explain how further generalization of this procedure naturally leads to K3 surfaces admitting double covers onto P2 branched along a plane sextic curve.
(This is joint work with Chuck Doran, University of Alberta)