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

Abstract

We 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.

32 pages

References in corpus (16)

• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• On Geometry and Matrix Models
• Phases of N=1 Supersymmetric Gauge Theories and Matrices
• Chiral Rings and Phases of Supersymmetric Gauge Theories
• An Introduction to Supersymmetric Gauge Theories and Matrix Models
• Exact Superpotentials from Matrix Models
• Quantum moduli spaces from matrix models
• The Curve of Compactified 6D Gauge Theories and Integrable Systems
• Adding flavor to Dijkgraaf-Vafa
• Five-Dimensional Gauge Theories and Quantum Mechanical Matrix Models
• Nonperturbative Superpotentials and Compactification to Three Dimensions
• Critical Points of Glueball Superpotentials and Equilibria of Integrable Systems
• Matrix Model Description of Baryonic Deformations
• N=1* in 5 dimensions: Dijkgraaf-Vafa meets Polchinski-Strassler
• On the Geometry of Matrix Models for N=1*
• On Effective Superpotentials and Compactification to Three Dimensions

Cited by in corpus (1)

• Non-Supersymmetric String Theory