High Energy Theory Seminar
In general relativity, there are no local observables, because the outcomes for measurements of space and time depend themselves on the strength of the gravitational field. Yet, there are quasi-local observables, which assign gravitational charges (e.g. momentum, angular momentum and centre of mass) to a two-dimensional entangling surface (separating the observer from the system observed). A very convincing argument for the positivity and monotonicity of the quasi-local free energy in certain regions of asymptotic AdS — regions which are bounded by a disk at infinity and a Ryu--Takayanagi extremal surface reaching into the bulk — has been given recently by Lashkari, Lin, Ooguri, Stoica and Van Raamsdonk [arXiv:1605.01075v1]. Spinors offer powerful tools to prove such inequalities in classical general relativity. In my talk, I will present recent progress in deriving balance and monotonicity laws for Ooguri's quasi-local definition of free energy using a twistorial generalisation of Witten's three-surface spinor equation. These spinors are surprisingly similar to certain two-surface spinors, which appear in loop quantum gravity when coupling bulk holonomies to a two-dimensional boundary [arXiv:1407.0025, 1107.5002]. I will discuss possible relations and applications.