Entropy, Contact Interaction with Horizon and Dark Energy

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.