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On Monopoles and Domain Walls

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Abstract

The purpose of this paper is to describe a relationship between maximally supersymmetric domain walls and magnetic monopoles. We show that the moduli space of domain walls in non-abelian gauge theories with N flavors is isomorphic to a complex, middle dimensional, submanifold of the moduli space of U(N) magnetic monopoles. This submanifold is defined by the fixed point set of a circle action rotating the monopoles in the plane. To derive this result we present a D-brane construction of domain walls, yielding a description of their dynamics in terms of truncated Nahm equations. The physical explanation for the relationship lies in the fact that domain walls, in the guise of kinks on a vortex string, correspond to magnetic monopoles confined by the Meissner effect.

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Authors and Affiliations

  1. Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Amihay Hanany

  2. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK

    David Tong

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  1. Amihay Hanany
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  2. David Tong
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Correspondence to David Tong.

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Communicated by N.A. Nekrasov

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Hanany, A., Tong, D. On Monopoles and Domain Walls. Commun. Math. Phys. 266, 647–663 (2006). https://doi.org/10.1007/s00220-006-0056-7

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