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Entanglement Entropy and TT[over ¯] Deformation.

William Donnelly1, Vasudev Shyam1

  • 1Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario N2L 2Y5, Canada.

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This study validates the conjecture that quantum gravity in finite spacetime regions is dual to a deformed conformal field theory (CFT). The TT[over ¯] deformation acts as an ultraviolet cutoff, matching entanglement entropy predictions.

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • String Theory
  • Holography

Background:

  • The conjecture posits a duality between quantum gravity in finite spacetime regions and a specific type of deformed conformal field theory (CFT).
  • Entanglement entropy is a key observable sensitive to ultraviolet (UV) physics and bulk geometry in holographic theories.

Purpose of the Study:

  • To test the conjecture relating finite region quantum gravity to TT[over ¯]-deformed CFTs using entanglement entropy.
  • To investigate the role of the TT[over ¯] deformation as a UV cutoff in holographic entanglement entropy calculations.

Main Methods:

  • Calculation of entanglement entropy for specific boundary states in the deformed CFT.
  • Application of the Ryu-Takayanagi formula to finite regions of the proposed dual bulk geometry.
  • Analysis of conical entropies to verify theoretical conjectures.

Main Results:

  • Entanglement entropy for antipodal points on a sphere is finite and matches predictions from the Ryu-Takayanagi formula in a finite region.
  • A family of conical entropies are finite, verifying a conjecture by Dong.
  • The TT[over ¯] deformation effectively acts as an ultraviolet cutoff for entanglement entropy.

Conclusions:

  • The results strongly support the conjecture that TT[over ¯]-deformed CFTs are holographic duals of finite spacetime regions.
  • The TT[over ¯] deformation provides a mechanism for regulating UV divergences in holographic entanglement entropy.