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Conformal Bounds in Three Dimensions from Entanglement Entropy.

Pablo Bueno1, Horacio Casini2, Oscar Lasso Andino3

  • 1Departament de Física Quàntica i Astrofísica, Institut de Ciències del Cosmos Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.

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|November 13, 2023
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Summary
This summary is machine-generated.

We propose bounds for entanglement entropy in three-dimensional conformal field theories (CFTs). These bounds, relating the universal coefficient F(A) to the minimal value F₀, are supported by evidence across various CFT models.

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • String Theory

Background:

  • Entanglement entropy in conformal field theories (CFTs) possesses a universal constant coefficient, F(A), for any spacetime region A.
  • This coefficient F(A) is minimized for a round disk region, denoted F₀, which equals the Euclidean free energy on a sphere.
  • Understanding these coefficients provides insights into the fundamental properties of quantum field theories.

Purpose of the Study:

  • To conjecture and provide evidence for bounds on the ratio F(A)/F₀ in three-dimensional CFTs.
  • To explore the implications of these bounds for other CFT characteristic constants, specifically the stress-tensor two-point function coefficient (Cₜ).
  • To establish an analogy with four-dimensional CFTs and the Hofman-Maldacena bounds.

Main Methods:

  • Formulating a conjecture bounding F(A)/F₀ by free scalar and Maxwell field results.
  • Providing strong theoretical evidence and analytical arguments to support the conjecture.
  • Investigating the derived bounds on the ratio Cₜ/F₀ for various CFTs.

Main Results:

  • The conjecture on F(A)/F₀ is supported by substantial evidence.
  • An analogous conjecture in 4D CFTs is shown to be equivalent to the Hofman-Maldacena bounds.
  • A universal upper bound Cₜ/F₀ ≤ 3/(4π²log2 - 6ζ[3]) ≈ 0.14887 is derived for 3D CFTs.

Conclusions:

  • The derived bounds offer new constraints on CFT properties.
  • The bound Cₜ/F₀ is verified for a wide range of theories including free scalars/fermions, O(N) and Gross-Neveu models, holographic theories, N=2 Wess-Zumino models, and ABJM theories.
  • The study reinforces the utility of entanglement entropy as a probe of quantum field theory structure.