  We show that certain 3D multi-gap topological insulators can host quantized
shift photoconductivities due to bulk invariants that are defined under reality
conditions imposed by additional symmetries. We recast the quantization in
terms of the integrated torsion tensor and the non-Abelian Berry connection
constituting Chern-Simons forms. Physically, we recognize that the topological
quantization emerges purely from virtual transitions contributing to the
optical response. Our findings provide another quantized electromagnetic DC
response due to the non-trivial band topology, beyond the quantum anomalous
Hall effect of Chern insulators and quantized circular photogalvanic effect
found in Weyl semimetals.
