Non-renormalization theorem in a lattice supersymmetric theory and the cyclic Leibniz rule

Abstract

N=4 supersymmetric quantum mechanical model is formulated on the lattice. Two supercharges, among four, are exactly conserved with the help of the cyclic Leibniz rule without spoiling the locality. In use of the cohomological argument, any possible local terms of the effective action are classified into two categories which we call type-I and type-II, analogous to the D- and F-terms in the supersymmetric field theories. We prove non-renormalization theorem on the type-II terms which include mass and interaction terms with keeping a lattice constant finite, while type-I terms such as the kinetic terms have nontrivial quantum corrections.

38 pages, 9 figures; (v2) Clarifying explanations added, refs and typos corrected

References in corpus (4)

• Deconstruction and other approaches to supersymmetric lattice field theories
• General solution of cyclic Leibniz rule
• Leibniz rule, locality and supersymmetry on lattice
• Non-renormalization theorem and cyclic Leibniz rule in lattice supersymmetry

Cited by in corpus (6)

• Progress and prospects of lattice supersymmetry
• Lattice studies of supersymmetric gauge theories
• Direct computational approach to lattice supersymmetric quantum mechanics
• Lattice study of supersymmetry breaking in N=2 supersymmetric quantum mechanics
• A lattice formulation of N=2 supersymmetric SYK model
• Numerical analyses of N=2 supersymmetric quantum mechanics with cyclic Leibniz rule on lattice