Entanglement entropy of a Rarita-Schwinger field in a sphere

Abstract

We study the universal logarithmic coefficient of the entanglement entropy 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.