  The Berry connection describes transformations induced by adiabatically
varying Hamiltonians. We study how zero modes of the modular Hamiltonian are
affected by varying the region that supplies the modular Hamiltonian. In the
vacuum of a 2d CFT, global conformal symmetry singles out a unique modular
Berry connection, which we compute directly and in the dual AdS$_3$ picture. In
certain cases, Wilson loops of the modular Berry connection compute lengths of
curves in AdS$_3$, reproducing the differential entropy formula. Modular Berry
transformations can be measured by bulk observers moving with varying
accelerations.
