High Energy Theory Seminar

Abstract: In this talk, I will introduce a geometric phase associated to a family of density matrices—the modular Berry phase. When computed in the boundary CFT, the modular Berry phase encodes geometric features of the dual spacetime. I will show that for a certain class of density matrices, the modular Berry phase is dual to an emergent bulk symplectic form, while in other cases it provides a direct measure of the local spacetime curvature. To make manifest that this quantity is well-defined in the large N limit, I will show how the discussion can be phrased in the language of operator algebras and the corresponding modular theory. Finally, I will demonstrate that the behavior of the Berry phase is sensitive to quantum chaotic features of the underlying theory, thus providing a novel probe for quantum chaos. These findings suggest a deep connection between geometric phases, modular chaos, and the local structure of spacetime.

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