Entanglement and Thermal Entropy of Gauge Fields

TL;DR

This paper investigates the universal logarithmic divergence in the entanglement entropy of gauge fields, resolving discrepancies in theoretical calculations by analyzing thermal entropy and modifying existing formulas for the energy-momentum tensor.

Contribution

It introduces a refined analysis of gauge field entanglement entropy, connecting it with thermal entropy on curved backgrounds and proposing modifications to established formulas.

Findings

Resolved discrepancy between free field calculation and Euler anomaly

Linked entanglement entropy divergence to thermal entropy on curved spaces

Proposed modifications to vacuum expectation value formulas for spin-1 energy-momentum tensor

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.