Define bulk entropy for gravitons on arbitrary regions

Determine whether the bulk effective-field-theory entropy S_eff for graviton excitations is well defined for an arbitrary spacetime subregion b, and, if so, establish a precise and consistent definition suitable for inclusion in the quantum extremal surface (QES) prescription for generalized entropy.

Background

In the QES prescription, the generalized entropy S_gen(b) includes a bulk entropy term S_eff(b) of quantum fields in the region b. While S_eff is standard for non-gravitational matter, the contribution from graviton excitations is subtle because gravitons are gauge fields and their local degrees of freedom and algebras in subregions are nontrivial to define.

The authors note that it is not currently settled whether S_eff can be consistently defined for gravitons on arbitrary regions, which directly impacts the rigorous application of the QES/island rule when gravitational fluctuations contribute to bulk entanglement.