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Matrix models, geometric engineering and elliptic genera
Journal of High Energy Physics, Volume: "03", Issue: 03, Pages: 069 - 069
Swansea University Author:
Timothy Hollowood
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DOI (Published version): 10.1088/1126-6708/2008/03/069
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...
| Published in: | Journal of High Energy Physics |
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| ISSN: | 1029-8479 |
| Published: |
2003
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| Online Access: |
Check full text
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| 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 |
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| College: |
Faculty of Science and Engineering |
| Issue: |
03 |
| Start Page: |
069 |
| End Page: |
069 |