Würzburg Seminar on Quantum Field Theory and Gravity

A major modern incarnation of the long-standing task of learning about the black hole interior is the study of complexity in holography. Despite a decade of interest from various communities, precise dualities between well-defined notions of complexity in bulk and boundary are exceedingly rare to find. In this light, this talk entails three core messages: 1) In sine dilaton gravity, the newly discovered bulk dual to the double scaled SYK model, we report a precise match between the extremal volume and Krylov spread complexity. This identification holds at finite temperature and in the quantum regime. A key lesson is that gravity demands to assign complexity also to Euclidean state preparation. 2) Investigating this dictionary carefully in its de Sitter limit, we show that, in this case, the extremal surface dual to boundary complexity is timelike and extends from past to future infinity. In higher dimensional dS, the analogous surface also exists and exhibits similar behavior, justifying this as a new candidate for holographic complexity in cosmological spacetimes. 3) Time permitting, we discuss work in progress on the properties of Krylov spread complexity in DSSYK obtained from the partition function in the semiclassical limit. This includes analytic insights into the early-time series, a critical examination of the infinite-temperature limit, and the possibility of analytic continuation beyond early times. Based on 2412.17785, 2510.13986, and work in progress.