Entanglement viscosity to entropy density ratio for spin-3/2 theory

TL;DR

This paper investigates the entanglement viscosity to entropy density ratio for spin-3/2 fields, revealing negative viscosity and entropy in RSA theory, and explores its conformal features.

Contribution

It extends the study of entanglement viscosity to higher-spin fields, specifically spin-3/2, and examines the ratio's behavior and underlying theory features.

Findings

Entanglement viscosity for spin-3/2 fields is negative.

Entropy density computed via modular Hamiltonian is negative.

The viscosity to entropy ratio saturates the KSS bound.

Abstract

It is known that the Minkowski vacuum appears as a thermal medium to an accelerated observer due to the renowned Unruh effect. More recently, it has been shown that at least for lower-spin fields this medium also exhibits a non-zero "entanglement" shear viscosity, which saturates the fundamental Kovtun-Son-Starinets (KSS) bound. We test the universality of this result for higher spins by computing the entanglement viscosity for spin-3/2 fields within the Rarita-Schwinger-Adler (RSA) theory. Strikingly, we obtain a negative viscosity. However, computing the entropy density using the modular Hamiltonian expansion method, we find it is also negative, and the viscosity to entropy ratio saturates the KSS bound. To clarify the origin of the negativity, we use another approach of Zubarev density operator, which gives positive entropy. We also show that RSA theory has many features of a conformal field theory.