Abstract
The entanglement entropy of an arbitrary spacetime region in a three-dimensional conformal field theory (CFT) contains a constant universal coefficient, . For general theories, the value of is minimized when is a round disk, , and in that case it coincides with the Euclidean free energy on the sphere. We conjecture that, for general CFTs, the quantity 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 for general CFTs. We verify the validity of this bound for free scalars and fermions, general and Gross-Neveu models, holographic theories, Wess-Zumino models and general ABJM theories.
- Received 31 July 2023
- Revised 8 September 2023
- Accepted 29 September 2023
DOI:https://doi.org/10.1103/PhysRevLett.131.171601
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.
Published by the American Physical Society