N=2 Wess-Zumino model on the d=2 Euclidean lattice

Abstract

We examine the N=2 Wess-Zumino model defined on the $d=2$ Euclidean lattice in connection with a restoration of the Leibniz rule in the limit $a\to 0$ in perturbatively finite theory. We are interested in the difference between the Wilson and Ginsparg-Wilson fermions and in the effects of extra interactions introduced by an analysis of Nicolai mapping. As for the Wilson fermion, it induces a linear divergence to individual tadpole diagrams in the limit $a\to 0$, which is absent in the Ginsparg-Wilson fermion. This divergence suggests that a careful choice of lattice regularization is required in a reliable numerical simulation. As for the effects of the extra couplings introduced by an analysis of Nicolai mapping, the extra couplings do not completely remedy the supersymmetry breaking in correlation functions induced by the failure of the Leibniz rule in perturbation theory, though those couplings ensure the vanishing of vacuum energy arising from disconnected diagrams. Supersymmetry in correlation functions is recovered in the limit $a\to 0$ {\em with or without} those extra couplings. In the context of lattice theory, it may be properly said that supersymmetry does not improve ultraviolet properties but rather it is well accommodated in theories with good ultraviolet properties.

24 pages. A reference was added. Appeared in Phys. Rev. D66 (2002) 074510

References in corpus (1)

• Supersymmetry on the lattice and the Leibniz rule

Cited by in corpus (27)

• Exact lattice supersymmetry
• A Lattice Formulation of Super Yang-Mills Theories with Exact Supersymmetry
• Super Yang-Mills Theories on the Two-Dimensional Lattice with Exact Supersymmetry
• Exact Extended Supersymmetry on a Lattice: Twisted N=4 Super Yang-Mills in Three Dimensions
• 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
• Simulations of $\mathcal{N}=2$ super Yang-Mills theory in two dimensions
• Two-dimensional N=(2,2) super Yang-Mills theory on the lattice via dimensional reduction
• Lattice Sigma Models with Exact Supersymmetry
• Taming the Leibniz Rule on the Lattice
• Supersymmetric nonperturbative formulation of the WZ model in lower dimensions
• Supersymetry on the Noncommutative Lattice
• Twisted SUSY Invariant Formulation of Chern-Simons Gauge Theory on a Lattice
• A local formulation of lattice Wess-Zumino model with exact $\U(1)_R$ symmetry
• Matrix formulation of superspace on 1D lattice with two supercharges
• Formulation of Supersymmetry on a Lattice as a Representation of a Deformed Superalgebra
• Three Dimensional N=2 Supersymmetry on the Lattice
• Multisupergravity from latticized extra dimension
• On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills
• Numerical simulation of the $\mathcal{N}=(2,2)$ Landau-Ginzburg model
• World-Line Path Integral Study of Supersymmetry Breaking in the Wess-Zumino Model
• Majorana fermions and CP-invariance of chiral gauge theories on the lattice