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Matrix models, geometric engineering and elliptic genera / Cumrun Vafa; Amer Iqbal; Timothy Hollowood

Journal of High Energy Physics, Volume: "03", Issue: 03, Pages: 069 - 069

Swansea University Author: Timothy, Hollowood

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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 i...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: 2003
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa28535
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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
College: College of Science
Issue: 03
Start Page: 069
End Page: 069