Modular Berry Connection

Abstract

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.

5 pages, 2 figures. Some clarifications added

References in corpus (2)

• Constructing local bulk observables in interacting AdS/CFT
• Holographic Holes and Differential Entropy

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