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Vortices, Instantons and Branes

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arxiv hep-th/0306150 v1 pith:IPZEU4O3 submitted 2003-06-17 hep-th

Vortices, Instantons and Branes

Amihay Hanany , David Tong This is my paper
classification hep-th
keywords vorticesmodulispaceinstantonsrelationshiptheoriesconstructiondescribe
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.

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