On the Noncommutativity Approach to Supersymmetry on the Lattice

Bruckmann, Falk; Kok, Mark de

doi:10.1063/1.2714361

Cited by 1 publication

(1 citation statement)

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“…An other approach in the same direction [15,19], attempts to preserve all the twisted supercharges on the lattice by introducing a non-trivial commutation relation between the coordinates in superspace. However, this formulation remains controversial after a recent paper [20] pointed out an inconsistency appearing in this method when applied to a toy quantum mechanical model. Finally, although the orbifolding and the twisting approaches appear different, Ünsal [21] recently showed that the former approach reproduces the twisted Yang-Mills theories in the continuum limit.…”

Section: Introductionmentioning

confidence: 99%

Twisted supersymmetric sigma model on the lattice

Catterall¹,

Ghadab

2006

J. High Energy Phys.

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In this paper we conduct a numerical study of the supersymmetric O(3) nonlinear sigma model. The lattice formulation we employ was derived in [1] and corresponds to a discretization of a twisted form of the continuum action. The twisting process exposes a nilpotent supercharge Q and allows the action to be rewritten in Q-exact form. These properties may be maintained on the lattice. We show how to deform the theory by the addition of potential terms which preserve the supersymmetry. A Wilson mass operator may be introduced in this way with a minimal breaking of supersymmetry. We additionally show how to rewrite the theory in the language of Kähler-Dirac fields and explain why this avenue does not provide a good route to discretization. Our numerical results provide strong evidence for a restoration of full supersymmetry in the continuum limit without fine tuning. We also observe a non-vanishing chiral condensate as expected from continuum instanton calculations.

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Section: Introductionmentioning

confidence: 99%