  Modular parallel transport is a generalization of Berry phases, applied to
modular (entanglement) Hamiltonians. Here we initiate the study of modular
parallel transport for disjoint field theory regions. We study modular parallel
transport in the kinematic space of multi-interval regions in the vacuum of
1+1-dimensional free fermion theory--one of the few theories for which modular
Hamiltonians on disjoint regions are known. We compute explicitly the
generators of modular parallel transport, and explain why their relatively
simple form follows from a half-sided modular inclusion. We also compute
explicitly the curvature two-form of modular parallel transport. We contrast
all calculations with the expected behavior of modular parallel transport in
holographic theories, emphasizing the role of non-local terms that couple
distinct intervals.
