Exotic theta terms in 2+1d fractonic φ-theory induce generalized Witten effects, with vortex operators gaining momentum subsystem charge (quadrupolar for the foliated case).
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A lattice formulation of the Atiyah-Patodi-Singer index is built using spectral flow of domain-wall Dirac operators generalized beyond product boundaries and proven to recover the continuum index for small enough lattice spacing.
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Exotic theta terms in 2+1d fractonic field theory
Exotic theta terms in 2+1d fractonic φ-theory induce generalized Witten effects, with vortex operators gaining momentum subsystem charge (quadrupolar for the foliated case).
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Capturing the Atiyah-Patodi-Singer index from the lattice
A lattice formulation of the Atiyah-Patodi-Singer index is built using spectral flow of domain-wall Dirac operators generalized beyond product boundaries and proven to recover the continuum index for small enough lattice spacing.