Fermion Actions extracted from Lattice Super Yang-Mills Theories

Abstract

We revisit 2D $\mathcal{N}=(2,2)$ super Yang-Mills lattice formulation (Sugino model) to investigate its fermion action with two (Majorana) fermion flavors and exact chiral-$U(1{)}_R$ symmetry. We show that the reconcilement of chiral symmetry and absence of further species-doubling originates in the 4D clifford algebra structure of the action, where 2D two flavors are spuriously treated as a single 4D four-spinor with four 4D gamma matrices introduced into kinetic and Wilson terms. This fermion construction based on the higher-dimensional clifford algebra is extended to four dimensions in two manners: (1) pseudo-8D sixteen-spinor treatment of 4D four flavors with eight 8D gamma matrices, (2) pseudo-6D eight-spinor treatment of 4D two flavors with five out of six 6D gamma matrices. We obtain 4D four-species and two-species lattice fermions with unbroken subgroup of chiral symmetry and other essential properties. We discuss their relations to staggered and Wilson twisted-mass fermions. We also discuss their potential feedback to 4D super Yang-Mills lattice formulations.

24 pages; references added, typos corrected

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• Lattice fermions as spectral graphs
• Equivalence of lattice operators and graph matrices
• New conjecture on exact Dirac zero-modes of lattice fermions
• Minimal-doubling and single-Weyl Hamiltonians
• Lattice fermion formulation via Physics-Informed Neural Networks: Ginsparg-Wilson relation and Overlap fermions