Matrix models, geometric engineering and elliptic genera

Oct, 2003
89 pages
Published in:
  • JHEP 03 (2008) 069
e-Print:
Report number:
  • HUTP-03-A074

Citations per year

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Abstract:
We compute the prepotential of N=2 supersymmetric gauge theories in four dimensions obtained by toroidal compactifications of gauge theories from 6 dimensions, as a function of Kahler and complex moduli of T^2. We use three different methods to obtain this: matrix models, geometric engineering and instanton calculus. Matrix model approach involves summing up planar diagrams of an associated gauge theory on T^2. Geometric engineering involves considering F-theory on elliptic threefolds, and using topological vertex to sum up worldsheet instantons. Instanton calculus involves computation of elliptic genera of instanton moduli spaces on R^4. We study the compactifications of N=2* theory in detail and establish equivalence of all these three approaches in this case. As a byproduct we geometrically engineer theories with massive adjoint fields. As one application, we show that the moduli space of mass deformed M5-branes wrapped on T^2 combines the Kahler and complex moduli of T^2 and the mass parameter into the period matrix of a genus 2 curve.
  • matrix model
  • gauge field theory: Yang-Mills
  • supersymmetry
  • dimension: 6
  • compactification: torus
  • dimension: 4
  • prepotential
  • Seiberg-Witten model
  • geometry: algebra
  • analytic properties
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