A Critique of the Link Approach to Exact Lattice Supersymmetry

Abstract

We examine the link approach to constructing a lattice theory of N=2 super Yang Mills theory in two dimensions. The goal of this construction is to provide a discretization of the continuum theory which preserves all supersymmetries at non-zero lattice spacing. We show that this approach suffers from an inconsistency and argue that a maximum of just one of the supersymmetries can be implemented on the lattice.

arXiv comment7 pages

References in corpus (19)

• 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
• Supersymmetry on a Euclidean Spacetime Lattice II: Theories with Eight Supercharges
• Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
• Exact Lattice Supersymmetry: the Two-Dimensional N=2 Wess-Zumino Model
• A geometrical approach to N=2 super Yang-Mills theory on the two dimensional lattice
• Twisted Supersymmetric Gauge Theories and Orbifold Lattices
• 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
• Deconstruction and other approaches to supersymmetric lattice field theories
• 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
• Lattice supersymmetry, superfields and renormalization
• Lattice Sigma Models with Exact Supersymmetry
• Noncommutativity Approach to Supersymmetry on the Lattice: SUSY Quantum Mechanics and an Inconsistency
• Lattice formulation of (2,2) supersymmetric gauge theories with matter fields

Cited by in corpus (24)

• Exact lattice supersymmetry
• Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions
• Classification of Supersymmetric Lattice Gauge Theories by Orbifolding
• Relationship between various supersymmetric lattice models
• Lattice Supersymmetry: Equivalence between the Link Approach and Orbifolding
• Taming the Leibniz Rule on the Lattice
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• Relations among Supersymmetric Lattice Gauge Theories via Orbifolding
• Two-dimensional N=(2,2) Supersymmetric Lattice Gauge Theory with Matter Fields in the Fundamental Representation
• Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice
• Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations
• Species Doublers as Super Multiplets in Lattice Supersymmetry: Exact Supersymmetry with Interactions for D=1 N=2
• Matrix formulation of superspace on 1D lattice with two supercharges
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• Exact Lattice Supersymmetry at the Quantum Level for $N=2$ Wess-Zumino Models in 1- and 2-Dimensions
• Species Doublers as Super Multiplets in Lattice Supersymmetry: Chiral Conditions of Wess-Zumino Model for D=N=2
• Exact Vacuum Energy of Orbifold Lattice Theories
• On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills
• An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry
• Deformed matrix models, supersymmetric lattice twists and N=1/4 supersymmetry
• Advances and applications of lattice supersymmetry
• Scalar Supersymmetry
• 3d N=4 Super-Yang-Mills on a Lattice
• Lattice supersymmetry in 1D with two supercharges