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Department of Mathematical Sciences

Seminar Archives

On this page you can find information about seminars in this and previous academic years, where available on the database.

Maths HEP Lunchtime Seminars: N=2 super Yang-Mills and the Geometry of Magnetic Monopoles

Presented by Andy Royston,

21 October 2016 13:00 in CM221

In this talk we consider BPS states in 4D, N=2 gauge theory in the presence of defects. We give a semiclassical description of these `framed BPS states' in terms of kernels of
Dirac operators on moduli spaces of singular monopoles. For both framed and ordinary BPS states we present a conjectural map between the data of the semiclassical construction and the data of the low-energy, quantum-exact Seiberg-Witten description. This map incorporates both perturbative and nonperturbative field theory corrections to the supersymmetric quantum mechanics of the monopole collective coordinates. We use it to translate recent developments in the study of N=2 theories, including wall-crossing formulae and the no-exotics theorem, into geometric statements about the Dirac kernels. The no-exotics theorem implies a broad generalization of Sen's conjecture concerning the existence of L^2 harmonic forms on monopole moduli space. This talk is based on work done in collaboration with Greg Moore and Dieter Van den Bleeken.

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