Entanglement entropy of a Rarita-Schwinger field in a sphere

TL;DR

This paper investigates the universal logarithmic coefficient of entanglement entropy for free fermionic fields, specifically spin-1/2 and spin-3/2 fields, in four-dimensional Minkowski space, revealing new universal coefficients and their physical implications.

Contribution

It computes the universal logarithmic coefficient of EE for the Rarita-Schwinger field, extending previous results for spin-1/2 fields, and discusses the physical meaning for higher spin theories.

Findings

Universal coefficient for spin-1/2 field: -11/90

Universal coefficient for spin-3/2 (Rarita-Schwinger) field: -71/90

Divergence in area coefficient with radial discretization, finite with geometric regularization

Abstract

We study the universal logarithmic coefficient of the entanglement entropy (EE) in a sphere for free fermionic field theories in a $d=4$ Minkowski spacetime. As a warm-up, we revisit the free massless spin-$1/2$ field case by employing a dimensional reduction to the $d=2$ half-line and a subsequent numerical real-time computation on a lattice. Surprisingly, the area coefficient diverges for a radial discretization but is finite for a geometric regularization induced by the mutual information. The resultant universal logarithmic coefficient $-11/90$ is consistent with the literature. For the free massless spin-$3/2$ field, the Rarita-Schwinger field, we also perform a dimensional reduction to the half-line. The reduced Hamiltonian coincides with the spin-$1/2$ one, except for the omission of the lowest total angular momentum modes. This gives a universal logarithmic coefficient of $-71/90$. We discuss the physical interpretation of the universal logarithmic coefficient for free higher spin field theories without a stress-energy tensor.