No-Go Theorem of Leibniz Rule and Supersymmetry on the Lattice

Details No-Go Theorem of Leibniz Rule and Supersymmetry on the Lattice No-Go Theorem of Leibniz Rule and Supersymmetry on the Lattice

2008-10-14

arxiv.org/abs/0810.2360v1

PoS LATTICE2008:233,2008

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, Proceedings of The XXVI International Symposium on Lattice Field Theory, July 14-19 2008, Williamsburg, Virginia, USA

Scientific paper

An obstacle to realize supersymmetry on a lattice is the breakdown of Leibniz rule. We give a proof of a no-go theorem that it is impossible to construct a lattice field theory in an infinite lattice volume with any nontrivial field products and difference operators that satisfy the following three properties: (i) translation invariance, (ii) locality and (iii) Leibniz rule. We then propose a way to escape from the no-go theorem by introducing infinite flavors, and present a lattice model of N=2 supersymmetric quantum mechanics equipped with the full exact supersymmetry.

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