Twisted Six Dimensional Gauge Theories on Tori, Matrix Models, and Integrable Systems

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dc.creatorGanguli, Surya
dc.creatorGanor, Ori J.
dc.creatorGill, James A.
dc.date2003-11-05
dc.date2004-06-02
dc.date.accessioned2026-07-07T10:49:46Z
dc.date.available2026-07-07T10:49:46Z
dc.descriptionWe use the Dijkgraaf-Vafa technique to study massive vacua of 6D SU(N) SYM theories on tori with R-symmetry twists. One finds a matrix model living on the compactification torus with a genus 2 spectral curve. The Jacobian of this curve is closely related to a twisted four torus T in which the Seiberg-Witten curves of the theory are embedded. We also analyze R-symmetry twists in a bundle with nontrivial first Chern class which yields intrinsically 6D SUSY breaking and a novel matrix integral whose eigenvalues float in a sea of background charge. Next we analyze the underlying integrable system of the theory, whose phase space we show to be a system of N-1 points on $T$. We write down an explicit set of Poisson commuting Hamiltonians for this system for arbitrary N and use them to prove that equilibrium configurations with respect to all Hamiltonians correspond to points in moduli space where the Seiberg-Witten curve maximally degenerates to genus 2, thereby recovering the matrix model spectral curve. We also write down a conjecture for a dual set of Poisson commuting variables which could shed light on a particle-like interpretation of the system.
dc.description32 pages
dc.identifierhttps://arxiv.org/abs/hep-th/0311042
dc.identifierhttp://arxiv.org/abs/hep-th/0311042
dc.identifierJHEP0409:014,2004
dc.identifierdoi:10.1088/1126-6708/2004/09/014
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/184330
dc.subjectHigh Energy Physics - Theory
dc.titleTwisted Six Dimensional Gauge Theories on Tori, Matrix Models, and Integrable Systems
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