Parity Anomaly as Modular Commutator with Massless Dirac Fermion
The modular commutator $J(A,B,C) = i\langle[K_{AB},K_{BC}]\rangle$ extracts the chiral central charge $c_-$ from a single bulk wavefunction of a \emph{gapped} 2d state, where $3J/\pi=c_-$. Inspired by the recent developments in the field of gapless symmetry-protected topological phases, we ask: what does the modular co...