Regularization of Non-commutative SYM by Orbifolds with Discrete Torsion and SL(2,Z) Duality

Abstract

We construct a nonperturbative regularization for Euclidean noncommutative supersymmetric Yang-Mills theories with four (N= (2,2)), eight (N= (4,4)) and sixteen (N= (8,8)) supercharges in two dimensions. The construction relies on orbifolds with discrete torsion, which allows noncommuting space dimensions to be generated dynamically from zero dimensional matrix model in the deconstruction limit. We also nonperturbatively prove that the twisted topological sectors of ordinary supersymmetric Yang-Mills theory are equivalent to a noncommutative field theory on the topologically trivial sector with reduced rank and quantized noncommutativity parameter. The key point of the proof is to reinterpret 't Hooft's twisted boundary condition as an orbifold with discrete torsion by lifting the lattice theory to a zero dimensional matrix theory.

36 pages, references added, minor typos fixed

References in corpus (5)

• A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges
• A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
• Twisted Superspace on a Lattice
• Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
• Exact Lattice Supersymmetry from Topological Field Theory

Cited by in corpus (13)

• Exact lattice supersymmetry
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• Relationship between various supersymmetric lattice models
• Large-N reduction in QCD with two adjoint Dirac fermions
• Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM
• On Matrix Model Formulations of Noncommutative Yang-Mills Theories
• Integrable Spin Chains on the Conformal Moose
• $\beta$-deformation for matrix model of M-theory
• Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry
• Matrix Orientifolding and Models with Four or Eight Supercharges
• Morita Equivalence of Noncommutative Supertori
• Large-N reduction with adjoint Wilson fermions
• Orientifolded Matrices and Supersymmetries that Give Rise to Spacetime Directional Asymmetry of Effective Interactions