Ginsparg-Wilson operators and a no-go theorem
Kazuo Fujikawa, Masato Ishibashi, Hiroshi Suzuki
TL;DR
This paper discusses limitations of Ginsparg-Wilson operators in lattice chiral gauge theories, highlighting a no-go theorem that shows CP symmetry breaking and issues with Majorana fermions at finite lattice spacing.
Contribution
It formulates a general no-go theorem demonstrating inherent symmetry and fermion definition issues in Ginsparg-Wilson operators for lattice chiral theories.
Findings
CP symmetry is broken at finite lattice spacing
Majorana fermions cannot be defined with chiral symmetric Yukawa couplings
Theorem applies broadly to Ginsparg-Wilson operators
Abstract
If one uses a general class of Ginsparg-Wilson operators, it is known that CP symmetry is spoiled in chiral gauge theory for a finite lattice spacing and the Majorana fermion is not defined in the presence of chiral symmetric Yukawa couplings. We summarize these properties in the form of a theorem for the general Ginsparg-Wilson relation.
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