Vortices, instantons and branes

Jun, 2003
33 pages
Published in:
  • JHEP 07 (2003) 037
e-Print:
Report number:
  • MIT-CTP-3388

Citations per year

200320092015202120250102030
Abstract:
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.
  • gauge field theory: U(N)
  • Higgs model
  • Hamiltonian formalism
  • vortex
  • instanton
  • membrane model
  • index theorem
  • moduli space
  • supersymmetry
  • differential geometry: noncommutative