Modular Berry Connection

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States of a CFT's subregions are consistent with a given global state. For a holographic CFT, this amounts to different entanglement wedges being patches of the same geometry. What relations between them make this possible?


I will propose a Berry experiment to study this question. Berry introduced a connection to describe transformations induced by adiabatically varying Hamiltonians. I will introduce a connection to study how the zero modes of a modular Hamiltonian are affected by varying the CFT subregion that supplies it. I will explain the geometric meaning of modular Berry phases in the bulk and describe an experiment to measure them which involves observers moving with adiabatically varying accelerations.