GP seminar: Operator algebraic AdS/CFT and subregion duality

Abstract: Employing operator algebra as an invariant of quantum field theory, I will present a novel formalism, capturing how the algebra of local operators of quantum field theory encodes information about spacetime regions, which I apply to investigate both quantum field theory and quantum gravity. In the context of AdS/CFT, I will present in my algebraic framework bulk reconstruction and relative entropy conservation, capture its quantum error correcting structure arising in the context of holographic spacetime, and discuss its significance. Motivated by a recent conjecture of Bousso et. al. on the bulk AdS description of boundary cocycle flow, I will characterize (approximate) complementary recovery in terms of (approximate) intertwining of bulk and boundary cocycle derivatives. This suggests that from algebraic perspective, the kink transform is precisely the bulk cocycle flow, which provides the bulk geometry via geometric modular action and the notion of time. Time permitting, I will further show using this new formalism that the aforementioned complementary recovery holds for Weyl algebras of Klein-Gordon fields in AdS wedges, yielding an operator algebraic version of subregion-subregion duality.

This is a seminar in the Centre of Geometry and Physics seminar series.