Entropy, Contact Interaction with Horizon and Dark Energy

TL;DR

This paper explores the connection between gauge configurations affecting entropy calculations in black holes, entanglement, and QCD, proposing a potential link to dark energy through non-dispersive topological effects.

Contribution

It identifies a common gauge configuration responsible for entropy mismatches in black holes, entanglement, and QCD, suggesting a unified topological origin.

Findings

The extra entropy term is non-dispersive and cannot be derived from spectral functions.

Gauge configurations responsible for entropy mismatch are linked to topological sectors in gauge theories.

Speculation that dark energy may originate from similar gauge configurations affecting entropy.

Abstract

We present some arguments suggesting that the mismatch between Bekenstein- Hawking entropy and the entropy of entanglement for vector fields is due to the same gauge configurations which saturate the contact term in topological susceptibility in QCD. In both cases the extra term with a "wrong sign" is due to distinct topological sectors in gauge theories. This extra term has non-dispersive nature, can not be restored from conventional spectral function through dispersion relations, and can not be associated with any physical propagating degrees of freedom. We make few comments on some profound consequences of our findings. In particular, we speculate that the source of the observed dark energy may also be related to the same type of gauge configurations which are responsible for the mismatch between black hole entropy and the entropy of entanglement in the presence of causal horizon.