Conformal bounds in three dimensions from entanglement entropy

TL;DR

This paper proposes bounds on the universal entanglement entropy coefficient in 3D CFTs, linking it to free scalar and Maxwell fields, and verifies these bounds across various theories including free, holographic, and supersymmetric models.

Contribution

It conjectures universal bounds on entanglement entropy ratios in 3D CFTs and provides evidence supporting these bounds across multiple theories.

Findings

Bound on $C_T / F_0$ is approximately 0.14887.

Bounds verified for free scalars, fermions, and various interacting theories.

Conjecture relates 3D bounds to 4D Hofman-Maldacena bounds.

Abstract

The entanglement entropy of an arbitrary spacetime region $A$ in a three-dimensional conformal field theory (CFT) contains a constant universal coefficient, $F(A)$. For general theories, the value of $F(A)$ is minimized when $A$ is a round disk, $F_0$, and in that case it coincides with the Euclidean free energy on the sphere. We conjecture that, for general CFTs, the quantity $F(A)/F_0$ is bounded above by the free scalar field result and below by the Maxwell field one. We provide strong evidence in favor of this claim and argue that an analogous conjecture in the four-dimensional case is equivalent to the Hofman-Maldacena bounds. In three dimensions, our conjecture gives rise to similar bounds on the quotients of various constants characterizing the CFT. In particular, it implies that the quotient of the stress-tensor two-point function coefficient and the sphere free energy satisfies $C_{ \scriptscriptstyle T} / F_0 \leq 3/ (4\pi^2 \log 2 - 6\zeta[3]) \simeq 0.14887$ for general CFTs. We verify the validity of this bound for free scalars and fermions, general $O(N)$ and Gross-Neveu models, holographic theories, $\mathcal{N}=2$ Wess-Zumino models and general ABJM theories.