Comments on Entanglement Negativity in Holographic Field Theories

TL;DR

This paper reviews entanglement negativity in relativistic quantum field theories, relating it to thermodynamic quantities and exploring its behavior in holographic and conformal field theories across dimensions.

Contribution

It provides a comprehensive overview of negativity, connects it to free energy differences in thermofield double states, and applies these insights to compute negativity in various CFTs, including holographic models.

Findings

Negativity of thermofield double states equals free energy difference at T and 2T.

Computed negativity for vacuum states in conformal field theories across multiple dimensions.

Discussed implications of negativity behavior in holographic field theories.

Abstract

We explore entanglement negativity, a measure of the distillable entanglement contained in a quantum state, in relativistic field theories in various dimensions. We first give a general overview of negativity and its properties and then explain a well known result relating (logarithmic) negativity of pure quantum states to the Renyi entropy (at index $1/2$), by exploiting the simple features of entanglement in thermal states. In particular, we show that the negativity of the thermofield double state is given by the free energy difference of the system at temperature $T$ and $2\,T$ respectively. We then use this result to compute the negativity in the vacuum state of conformal field theories in various dimensions, utilizing results that have been derived for free and holographic CFTs in the literature. We also comment upon general lessons to be learnt about negativity in holographic field theories.