GQFI-UGent-WST Seminar: Juan Pedraza "Lorentzian Threads and Holographic Complexity"
In this talk, Juan Pedraza (ICC Barcelona) uses the continuous min flow-max cut principle to reformulate the 'complexity=volume' conjecture using Lorentzian flows. Conceptually, discretized flows are interpreted in terms of `gatelines', one-dimensional time-like curves that connect layers of a tensor network grid in the bulk spacetime. Each gateline represents a unitary operation such that the bulk calculation for complexity matches its information-theoretic definition. The bulk symplectic potential provides a 'canonical' flow configuration characterizing perturbations around arbitrary CFT states. Its consistency requires the bulk to obey linearized Einstein's equations, which are shown to be equivalent to the holographic first law of complexity, thereby advocating a notion of 'spacetime complexity'. Finally, Juan explains the need for a more general measure of complexity that captures the role of suboptimal flows or tensor network configurations. Based on 2105.12735 and 2106.12585.
The Virtual Seminar Series “GQFI-Ghent University-Warsaw String Theory” (GQFI-UGent-WST) is a joint initiative between the strings/holography groups at the Albert Einstein Institute (AEI) in Potsdam, Ghent University and the University Warsaw. The calendar for upcoming GQFI-UGent-WST seminars can be found here: https://gqfi.aei.mpg.de/node/3.
This talk is primarily based on arXiv:2105.12735 [hep-th] (https://arxiv.org/abs/2105.12735) and arXiv:2106.12585 [hep-th] (https://arxiv.org/abs/2106.12585).
This talk was recorded on December 14th, 2021 at the Albert Einstein Institute in Potsdam-Golm.