Conformal Bounds in Three Dimensions from Entanglement Entropy

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.