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Modular Berry Connection for Entangled Subregions in AdS/CFT.

Bartłomiej Czech1, Lampros Lamprou2, Samuel McCandlish3

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|March 17, 2018
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Summary
This summary is machine-generated.

This study explores the modular Berry connection in 2D conformal field theory and its 3D anti-de Sitter (AdS3) dual. It reveals how this connection relates to geometric quantities and can be measured by observers in the bulk.

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Area of Science:

  • Quantum Field Theory
  • String Theory
  • AdS/CFT Correspondence

Background:

  • The Berry connection describes transformations in quantum systems with varying parameters.
  • Modular Hamiltonians are crucial in quantum information and field theory, particularly in understanding entanglement and spacetime geometry.

Purpose of the Study:

  • To investigate the behavior of zero modes of the modular Hamiltonian under changes in its defining region.
  • To compute the modular Berry connection in a 2D conformal field theory vacuum and its dual 3D anti-de Sitter (AdS3) spacetime.
  • To explore the relationship between Wilson loops of the modular Berry connection and geometric quantities in AdS3.

Main Methods:

  • Direct computation of the modular Berry connection in a 2D conformal field theory.
  • Utilizing the dual 3D anti-de Sitter (AdS3) picture to analyze the connection.
  • Calculating Wilson loops of the modular Berry connection.

Main Results:

  • A unique modular Berry connection is identified in the 2D conformal field theory vacuum, arising from global conformal symmetry.
  • In specific instances, Wilson loops of this connection yield lengths of curves in AdS3, aligning with the differential entropy formula.
  • Modular Berry transformations are shown to be measurable by observers in the AdS3 bulk experiencing varying accelerations.

Conclusions:

  • The study establishes a direct link between quantum field theory concepts (modular Berry connection) and geometric properties in a holographic dual (AdS3).
  • This work provides a framework for measuring quantum information-theoretic quantities through geometric observations in a gravitational context.
  • The findings contribute to understanding the interplay between quantum entanglement, spacetime geometry, and holographic duality.