Department of Mathematics

Mathematical Physics and Gauge Theory

  •  BPS monopoles with non-maximal symmetry breaking and the Nahm transform
  •  10/03/2017
  •  11:00 AM - 12:00 PM
  •  C304 Wells Hall
  •  Akos Nagy, Fields Institute/University of Waterloo

The notion of “broken symmetry” is central in gauge theories. For BPS monopoles, symmetry breaking can be defined in terms of the eigenvalues of the Higgs-field at infinity. The symmetry breaking is maximal if the eigenvalues are distinct. Monopoles with maximal symmetry breaking have been studied extensively by both mathematicians and physicists for decades now, but little is known about the general case. In this talk, I will show how to produce monopoles with arbitrary symmetry breaking using the Nahm transform, and I will also outline the construction of its inverse. The inversion heavily uses first order elliptic PDE's on non-compact spaces, more concretely, the theory of Callias-type operators in 3D. This is a joint project with Benoit Charbonneau.



Department of Mathematics
Michigan State University
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C212 Wells Hall
East Lansing, MI 48824

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