Do gauge fields really contribute negatively to black hole entropy?

TL;DR

The paper investigates whether gauge fields contribute negatively to black hole entropy via Kabat's contact term, which would renormalize $1/G$ with $c_1 = (D-2)/6 - 1$. It uses the conical-entropy framework and heat-kernel methods to derive the Kabat term for Maxwell fields and then tests the issue in two dimensions using smooth compact manifolds and reduced phase-space quantization to isolate physical degrees of freedom. The main result is that in $D=2$, Maxwell entropy is positive, finite, and equals the entanglement entropy, with no $1/G$ renormalization, implying the Kabat term is not physical in this setting. These findings challenge the notion of gravitational antiscreening by gauge fields and motivate reexamining higher-dimensional analyses with careful infrared and gauge considerations.

Abstract

Quantum fluctuations of matter fields contribute to the thermal entropy of black holes. For free minimally-coupled scalar and spinor fields, this contribution is precisely the entanglement entropy. For gauge fields, Kabat found an extra negative divergent "contact term" with no known statistical interpretation. We compare this contact term to a similar term that arises for nonminimally-coupled scalar fields. Although both divergences may be interpreted as terms in the Wald entropy, we point out that the contact term for gauge fields comes from a gauge-dependent ambiguity in Wald's formula. Revisiting Kabat's derivation of the contact term, we show that it is sensitive to the treatment of infrared modes. To explore these infrared issues, we consider two-dimensional compact manifolds, such as Euclidean de Sitter space, and show that the contact term arises from an incorrect treatment of zero modes. In a manifestly gauge-invariant reduced phase space quantization, the gauge field contribution to the entropy is positive, finite, and equal to the entanglement entropy.