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UNIVERSITY OF CALIFORNIA, SANTA BARBARA BERKELEY DAVIS IRVINE LOS ANGELES MERCED RIVERSIDE SAN DIEGO SAN FRANCISCO
 

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 Seiberg-Witten curve
Andreas Malmendier
UCSB
Friday, October 5, 2007, 4:00 p.m.
Room 6635 South Hall
Abstract: We show that the Seiberg-Witten family of elliptic curves defines a four-
dimensional, Jacobian rational elliptic surface Z over the u-plane 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 rank-two holomorphic SU(2)/Z2-bundles 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 non-trivial 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

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics