Theory Group Seminar, 14 November 2017
Bartek Czech, IAS, Princeton
Modular Berry Connection
Many quantities in the AdS/CFT correspondence, for example entanglement entropies, are defined up to a choice of UV cutoff. The cutoff can be chosen and adjusted depending on one's purposes; it represents a sort of gauge freedom. I will explain that this gauge freedom leads to physical consequences in a way that closely mirrors the construction of the Berry phase. In Berry's language, the control space is the kinematic space (the space of pairs of points) in CFT2 and the changing Hamiltonians are the modular Hamiltonians of the intervals. The modular Berry "phase" is actually a "Berry normalization"; it acts on OPE blocks / geodesic operators in the bulk of AdS3 by a multiplicative constant, which equals (the exponential of) the length of the bulk curve selected by a given closed trajectory in kinematic space. I will sketch a few generalizations and potential applications of modular Berry phases.