Entanglement entropy of a Rarita-Schwinger field in a sphere

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.

19 pages + Appendices, 4 figures

References in corpus (21)

• Towards a derivation of holographic entanglement entropy
• Entanglement entropy, conformal invariance and extrinsic geometry
• Entropic order parameters for the phases of QFT
• Area law and vacuum reordering in harmonic networks
• Entanglement Entropy in (3+1)-d Free $U(1)$ Gauge Theory
• Area terms in entanglement entropy
• Gravity as a gapless phase and biform symmetries
• Distributions in CFT II. Minkowski Space
• Irreversibility, QNEC, and defects
• Generalized Symmetries of the Graviton
• Recurrence and differential relations for spherical spinors
• Entanglement entropy of gravitational edge modes
• On the logarithmic coefficient of the entanglement entropy of a Maxwell field
• Entanglement entropy of linearized gravitons in a sphere
• Canonical Field Anticommutators in the Extended Gauged Rarita-Schwinger Theory
• Hyperbolic cylinders and entanglement entropy: gravitons, higher spins, $p$-forms
• Modular Hamiltonian of the scalar field in the semi infinite line: dimensional reduction for spherically symmetric regions
• Scale vs. Conformal Invariance at the IR Fixed Point of Quantum Gravity
• Aspects of quantum information in finite density field theory
• Charges in the UV completion of neutral electrodynamics
• Holographic entanglement entropy inequalities beyond strong subadditivity

Cited by in corpus (2)

• New conformal-like symmetry of strictly massless fermions in four-dimensional de Sitter space
• Scale and Conformal Invariance on (A)dS