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arXiv · 0709.4446

Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions

Robbert Dijkgraaf·Lotte Hollands·Piotr Sulkowski·Cumrun Vafa
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Abstract

We show that various holomorphic quantities in supersymmetric gauge theories can be conveniently computed by configurations of D4-branes and D6-branes. These D-branes intersect along a Riemann surface that is described by a holomorphic curve in a complex surface. The resulting I-brane carries two-dimensional chiral fermions on its world-volume. This system can be mapped directly to the topological string on a large class of non-compact Calabi-Yau manifolds. Inclusion of the string coupling constant corresponds to turning on a constant B-field on the complex surface, which makes this space non-commutative. Including all string loop corrections the free fermion theory is elegantly formulated in terms of holonomic D-modules that replace the classical holomorphic curve in the quantum case.

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Robbert Dijkgraaf, Lotte Hollands, Piotr Sulkowski, Cumrun Vafa. 2007-09-27. Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions. https://doi.org/10.1088/1126-6708%2F2008%2F02%2F106

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