Speaker: Dr. Zhencheng Wang (UIUC，USA)

Time: 9:30 on Friday, Dec. 1st, 2023

Location: Online(Tencent Conference number: 595-491-048)

Abstract: The AdS/CFT correspondence states that certain conformal field theories are equivalent to quantum gravity theories in a higher-dimensional anti-de Sitter space. On the CFT side of the correspondence, any two positive operators A, B will satisfy the trace inequality Tr(AB) ≤ Tr(A) Tr(B). This relation holds on any Hilbert space H and is deeply associated with the fact that the algebra B(H) of bounded operators on H is a type I von Neumann factor. Holographic bulk theories must thus satisfy a corresponding condition, which we investigate. In particular, we argue that the Euclidean gravitational path integral respects this inequality at all orders in the semi-classical expansion and with arbitrary higher-derivative corrections. The argument relies on a conjectured property of the classical gravitational action, which in particular implies a positive action conjecture for quantum gravity wavefunctions. We prove this conjecture for Jackiw-Teitelboim gravity and we also motivate it for more general theories.