Relations among Supersymmetric Lattice Gauge Theories via Orbifolding

Abstract

We show how to derive Catterall's supersymmetric lattice gauge theories directly from the general principle of orbifolding followed by a variant of the usual deconstruction. These theories are forced to be complexified due to a clash between charge assignments under U(1)-symmetries and lattice assignments in terms of scalar, vector and tensor components for the fermions. Other prescriptions for how to discretize the theory follow automatically by orbifolding and deconstruction. We find that Catterall's complexified model for the two-dimensional N=(2,2) theory has two independent preserved supersymmetries. We comment on consistent truncations to lattice theories without this complexification and with the correct continuum limit. The construction of lattice theories this way is general, and can be used to derive new supersymmetric lattice theories through the orbifolding procedure. As an example, we apply the prescription to topologically twisted four-dimensional N=2 supersymmetric Yang-Mills theory. We show that a consistent truncation is closely related to the lattice formulation previously given by Sugino.

arXiv comment20 pages, LaTeX2e, no figure

References in corpus (19)

• (De)Constructing Dimensions
• Supersymmetry on a Spatial Lattice
• Supersymmetry on a Euclidean Spacetime Lattice I: A Target Theory with Four Supercharges
• A Euclidean Lattice Construction of Supersymmetric Yang-Mills Theories with Sixteen Supercharges
• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
• Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
• Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
• Lattice Supersymmetry and Topological Field Theory
• Twisted Superspace on a Lattice
• Exact Extended Supersymmetry on a Lattice: Twisted N=2 Super Yang-Mills in Two Dimensions
• Various Super Yang-Mills Theories with Exact Supersymmetry on the Lattice
• Lattice formulation of $\mathcal{N}=4$ super Yang-Mills theory
• Two-Dimensional Compact N=(2,2) Lattice Super Yang-Mills Theory with Exact Supersymmetry
• Non-positive fermion determinants in lattice supersymmetry
• Simulations of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions
• A Critique of the Link Approach to Exact Lattice Supersymmetry
• Noncommutativity Approach to Supersymmetry on the Lattice: SUSY Quantum Mechanics and an Inconsistency

Cited by in corpus (28)

• SU(N) gauge theories at large N
• Exact lattice supersymmetry
• From Twisted Supersymmetry to Orbifold Lattices
• Restoration of supersymmetry on the lattice: Two-dimensional $\mathcal{N}=(2,2)$ supersymmetric Yang-Mills theory
• Geometry of Orbifolded Supersymmetric Lattice Gauge Theories
• Perturbative renormalization of lattice N=4 super Yang-Mills theory
• A proposal of a fine tuning free formulation of 4d N=4 super Yang-Mills
• First results from simulations of supersymmetric lattices
• Phase Structure of Lattice N=4 Super Yang-Mills
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• On the sign problem in 2D lattice super Yang--Mills
• Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry
• Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice
• Lattice formulation of 2D $\mathcal{N}=(2,2)$ SQCD based on the B model twist
• An object oriented code for simulating supersymmetric Yang--Mills theories
• Lattice Actions for Yang-Mills Quantum Mechanics with Exact Supersymmetry
• Exact Lattice Supersymmetry at the Quantum Level for $N=2$ Wess-Zumino Models in 1- and 2-Dimensions
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• Anomaly and Sign problem in $\mathcal{N}=(2,2)$ SYM on Polyhedra : Numerical Analysis
• Exact Vacuum Energy of Orbifold Lattice Theories
• On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills
• Mass spectrum of $2$-dimensional $\mathcal{N}=(2,2)$ super Yang-Mills theory on the lattice
• Supersymmetric Gauge Theory on the Graph
• An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry
• Gradient flow representation of the four-dimensional $\mathcal{N}=2$ super Yang--Mills supercurrent
• Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry
• Vafa-Witten Theory on N=2 and N=4 Twisted Superspace in Four Dimensions
• An anisotropic hybrid non-perturbative formulation for 4D N = 2 supersymmetric Yang-Mills theories