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

10/14 2020
  • Title (Seminar) Kinematic Space in AdS3/CFT2: How Bulk Lengths and Boosts are Entanglement Berry Phases
  • Speaker
  • Date
  • Venue
    • Abstract

    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.