Generalising the Ginsparg-Wilson relation: Lattice Supersymmetry from Blocking Transformations

Abstract

The Ginsparg-Wilson relation is extended to interacting field theories with general linear symmetries. Our relation encodes the remnant of the original symmetry in terms of the blocked fields and guides the construction of invariant lattice actions. We apply this approach in the case of lattice supersymmetry. An additional constraint has to be satisfied because of the appearance of a derivative operator in the symmetry transformations. The solution of this constraint leads to non-local SLAC-type derivatives. We investigate the corresponding kinetic operators on the lattice within an exact solution of supersymmetric quantum mechanics. These solutions - analogues of the overlap operator for supersymmetry - can be made local through a specific choice of the blocking kernel. We show that the corresponding relation allows for local lattice symmetry operators as well as local lattice actions. We argue that for interacting theories the lattice action is polynomial in the fields only under special circumstances, which is exemplified within an exact solution.

24 pages, 3 figures

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• Critical flavour number of the Thirring model in three dimensions
• Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry
• Supersymmetry on the lattice
• 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
• Blocking-inspired supersymmetric actions: a status report
• Species Doublers as Super Multiplets in Lattice Supersymmetry: Chiral Conditions of Wess-Zumino Model for D=N=2
• A renormalisation group derivation of the overlap formulation
• Improved lattice actions for supersymmetric quantum mechanics
• Generalisations of the Ginsparg-Wilson relation and a remnant of supersymmetry on the lattice
• Supersymmetry on the lattice and the status of the Super-Yang-Mills simulations