Generalized Ginsparg-Wilson relations: Fermionic anomalies on the lattice

Conference · Fri Mar 07 04:00:00 EST 2025

DOI:https://doi.org/10.22323/1.466.0375· OSTI ID:2551811

Singh, Hersh ^[1]

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1. Fermilab

The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be generalized to Majorana or Dirac fermions in any dimension for finite symmetry transformations (continuous or discrete). We find an exact symmetry which reproduces both perturbative and global anomalies on the lattice. These generalized GW fermions are boundary theories of various bulk symmetry-protected topological phases and thus provide an explicit lattice realization of the fermionic bulk-boundary correspondence central to recent proposals for chiral gauge theories on the lattice.

• Research Organization: Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• DOE Contract Number: 89243024CSC000002
• OSTI ID: 2551811
• Report Number(s): FERMILAB-CONF-25-0062-T; arXiv:2503.05900; oai:inspirehep.net:2898308
• Country of Publication: United States
• Language: English