Entanglement and Thermal Entropy of Gauge Fields

TL;DR

The paper addresses the universal logarithmic term in the entanglement entropy of gauge fields and resolves a known spin-1 mismatch by performing a vector Laplacian heat-kernel analysis, revealing a necessary surface-term contribution. It uses the Casini mapping to relate entanglement entropy to thermal entropy on open Einstein space and on the static patch of de Sitter, showing that the log coefficient matches the Euler anomaly a when all contributions are properly accounted. At strong coupling, holographic (AdS/CFT) methods yield the same universal term for N=4 SYM, supporting the claimed universality and the proposed modifications to the spin-1 stress-energy tensor on conformally flat backgrounds. The work highlights the role of surface terms, such as Kabat’s contact term, in gauge-field entanglement and energy-momentum computations, pointing to a refined understanding of gauge degrees of freedom near entangling surfaces.

Abstract

We consider the universal logarithmic divergent term in the entanglement entropy of gauge fields in the Minkowski vacuum with an entangling sphere. Employing the mapping in arXiv:1102.0440, we analyze the corresponding thermal entropy on open Einstein universe and on the static patch of de Sitter. Using the heat kernel of the vector Laplacian we resolve a discrepancy between the free field calculation and the expected Euler conformal anomaly. The resolution suggests a modification of the well known formulas for the vacuum expectation value of the spin-1 energy-momentum tensor on conformally flat space-times.