# Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions

 Title: Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions Author: Dijkgraaf, Robbert; Hollands, Lotte; Sulkowski, Piotr; Vafa, C. Note: Order does not necessarily reflect citation order of authors. Citation: Dijkgraaf, Robbert, Lotte Hollands, Piotr Sulkowski, and Cumrun Vafa. 2008. Supersymmetric gauge theories, intersecting branes and free fermions. Journal of High Energy Physics 2008(02): 106. Full Text & Related Files: 0709.4446v2.pdf (619.5Kb; PDF) 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. Published Version: doi:10.1088/1126-6708/2008/02/106 Other Sources: http://arxiv.org/abs/0709.4446 Terms of Use: This article is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#OAP Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:8152243 Downloads of this work: