报告题目：A trace inequality for Euclidean gravitational path integrals (and a new positive action conjecture)

报告人：王振丞 博士（UIUC，USA）

时间：2023年12月1日（周五）     9：30

地点：线上腾讯会议(腾讯会议号：595-491-048)

摘要：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.