Reflection symmetry on twisted Dirac operators on warped cylinders holds precisely when 2A is integer, yielding unitary equivalence of APS blocks and an RO(O(2))-valued or mod-two spectral-flow invariant.
Capturing the Atiyah-Patodi-Singer index from the lattice
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We construct a formulation of the Atiyah-Patodi-Singer index of Dirac operators in lattice gauge theory for domains with compact boundaries in a flat torus. The key idea is to exploit its equality to the spectral flow of the domain-wall fermion Dirac operators, which we generalize in this work to cases without product structure near the boundary. We prove that, for sufficiently small lattice spacings, this formulation correctly captures the continuum Atiyah-Patodi-Singer index.
fields
math-ph 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Reflection Symmetry, APS Boundary Conditions, and Equivariant Spectral Flow on a Warped Cylinder
Reflection symmetry on twisted Dirac operators on warped cylinders holds precisely when 2A is integer, yielding unitary equivalence of APS blocks and an RO(O(2))-valued or mod-two spectral-flow invariant.