PoS - Proceedings of Science
Volume 430 - The 39th International Symposium on Lattice Field Theory (LATTICE2022) - Theoretical Developments
Reformulation of anomaly inflow on the lattice and construction of lattice chiral gauge theories
J. Pedersen* and Y. Kikukawa
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Pre-published on: January 24, 2023
Published on: April 06, 2023
We point out that the integrability condition for lattice chiral determinant of overlap Weyl fermion can be reformulated in parallel with the modern understanding of anomaly inflow based on Dai-Freed theorem and topological classification of global anomalies by bordism invariance.
The known relations of the (2n+1)- and (2n+2)-dim domain-wall fermions and (2n)- and (2n+1)-dim overlap fermions, respectively, imply that Dai-Freed theorem and Atiya-Patodi-Singer index theorem.
These relations also hold precisely true on the lattice, where the complex phase of (2n+1)-dim overlap fermion determinant defines the $\eta$-invariant.
This $\eta$-invariant becomes ``bordism invariant", if the local chiral anomaly density of the (2n+2)-dim overlap fermion is classified as ``cohomologically" trivial along with the perturbative condition of gauge anomaly cancellation. Then, the integrability condition is given simply by the fact that the exponentiate of lattice $\eta$-invariant square is strictly unity for any admissible (2n+1)-dim gauge-link fields.
DOI: https://doi.org/10.22323/1.430.0381
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