A solution to the fermion doubling problem for supersymmetric theories on the transverse lattice

Abstract

Species doubling is a problem that infects most numerical methods that use a spatial lattice. An understanding of species doubling can be found in the Nielsen-Ninomiya theorem which gives a set of conditions that require species doubling. The transverse lattice approach to solving field theories, which has at least one spatial lattice, fails one of the conditions of the Nielsen-Ninomiya theorem nevertheless one still finds species doubling for the standard Lagrangian formulation of the transverse lattice. We will show that the Supersymmetric Discrete Light Cone Quantization (SDLCQ) formulation of the transverse lattice does not have species doubling.

arXiv comment4 pages, v2: a reference and comments added, the version to appear in Phys. Rev. D

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Cited by in corpus (6)

• 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
• Twisted supersymmetric sigma model on the lattice
• Lattice Formulation of Two-Dimensional N=(2,2) SQCD with Exact Supersymmetry
• Ginsparg-Wilson Formulation of 2D N =(2,2) SQCD with Exact Lattice Supersymmetry
• N=1 super Yang-Mills on a (3+1) dimensional transverse lattice with one exact supersymmetry