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(Seminar) Kinematic Space in AdS3/CFT2: How Bulk Lengths and Boosts are Entanglement Berry Phases
2020-10-14  【 】【打印】【关闭

CAS Key Laboratory of Theoretical Physics

Institute of Theoretical Physics

Chinese Academy of Sciences

 online-Seminar

Title

题目

Kinematic Space in AdS3/CFT2: How Bulk Lengths and Boosts are Entanglement Berry Phases

Speaker

报告人

Bartek Czech

Affiliation

所在单位

IAS Tsinghua

Date

日期

Oct 14 (Wed), 15 (Thur), 2:00 pm

Venue

地点

南楼6620

http://live.xylink.com/live/v/9680cda074c5cf2e017511798c4f18c7

Contact Person

所内联系人

何颂

Abstract

摘要

I will review an alternative and often more powerful formalism for describing physics in AdS3 space: not as a mesh of points but as a fabric woven by geodesics. An illustrative example of statements enabled by this formalism is that the length of a curve equals the (properly defined) "number" of geodesics which intersect it. The main stage of the formalism is Kinematic Space: the space of geodesics or--equivalently--the space of CFT subregions. Each such CFT subregion is entangled with its complement; this entanglement defines the "modular Hamiltonian" of the subregion. A trajectory in Kinematic Space gives a family of smoothly varying modular Hamiltonians, which in turn defines a modular (entanglement) Berry phase. Virtually all geometric properties of the bulk--most of which had not been previously understood from the CFT point of view--are manifestations of entanglement Berry phases; this includes lengths of curves, the bulk Riemann curvature, even proper time registered by massive particles. The entanglement Berry phases are non-trivial because the entanglement Berry curvature is non-vanishing. In the simplest example the positivity of entanglement Berry curvature is equivalent to the strong subadditivity of entanglement entropy, which underscores novel and deep links between the emergence of the bulk in holography, quantum information theory, and the physics of Berry phases.
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