[HEG] Subregion algebras in classical and quantum gravity

Who: Venkatesa Chandrasekaran (Stanford University)

Title: Subregion algebras in classical and quantum gravity

Abstract: We study subregion algebras in classical and perturbative quantum gravity on half-spaces of event horizons.\ We construct half-sided supertranslation generators by extending subregion phase spaces of the event horizon to include doubled pairs of edge modes obtained from splitting the horizon.\ These edge modes carry a corner symplectic form that gives rise to canonical generators of half-sided boosts and translations, the former of which is the area operator.\ We show that the translation generator is necessarily two-sided in the edge modes.\ The charges act nontrivially on gravitationally dressed bulk observables, such that subalgebras take the form of a crossed product by the associated automorphism group.\ Quantizing the extended phase space after linearizing around a black hole, we obtain for each cut a Type II$_{\infty}$ von Neumann algebra whose entropy coincides with the generalized entropy of that cut.\ The integrability of the half-sided translation generator lifts to the existence of a self-adjoint operator that generates time evolution of the Type~II$_\infty$ subalgebras.\ The nesting property of the resulting one-parameter family of subalgebras implies a generalized second law for linearized perturbations of Killing horizons.\ Finally, we use gravitational half-sided modular inclusion algebras to prove quantum focusing along Killing horizons in the perturbative quantum gravity regime.