 
Summary: UNIVERSITY OF CALIFORNIA, SANTA BARBARA
BERKELEY · DAVIS · IRVINE · LOS ANGELES · MERCED · RIVERSIDE · SAN DIEGO · SAN FRANCISCO
CSANTA BARBARA · SANTA CRUZ
Geometry, Topology, and Physics Seminar
The topology and geometry of the SeibergWitten curve
Andreas Malmendier
UCSB
Friday, October 5, 2007, 4:00 p.m.
Room 6635 South Hall
Abstract: We show that the SeibergWitten family of elliptic curves defines a four
dimensional, Jacobian rational elliptic surface Z over the uplane with boundary
whose signature equals minus the number of massive hypermultiplets. The family of
the stable semiclassical BPS states defines a unique flat holomorphic line bundle on
Z. We also construct ranktwo holomorphic SU(2)/Z2bundles and show that the
central charges of the corresponding quantum states are half the charges of the BPS
states.
We show that the local anomaly of the determinant line bundle of the ¯operator
along the fiber of Z vanishes. We determine the nontrivial global anomaly as the
holonomy of the determinant section and the relation to the signature of Z. Moreover,
we show that the determinant line bundle extends across the nodal fibers of Z. The
