Space-time BCFT legos and RG flows

Friday 21 Feb 2025, 10:00 → 11:30 Asia/Tokyo

Date: February 21th (Fri), 10:00AM (JST)
Speaker: Ling-Yan Hung (Yau Mathematical Sciences Center, Tsinghua University)
Title: Space-time BCFT legos and RG flows

Abstract: Is it possible to read off the quantum gravity dual of a CFT directly from its operator algebra? In this talk, we present a step-by-step recipe synthesizing results and techniques from conformal bootstrap, topological symmetries, tensor networks, a novel symmetry-preserving real-space renormalization algorithm devised originally in lattice models,  and the asymptotics of quantum 6j symbols, thereby providing an answer in the affirmative. Quantum 2D Liouville theory serves as a simple and explicit example, illustrating how the quantum gravitational path integral can be built up from local pieces of BCFT correlation functions, which we call the ``BCFT Legos''.  If time allows, we will discuss how the bulk theory derived from TTbar flow of CFTs coincides with the bulk that emerges and how that follows from a general holographic principle that we summarize as symQRG = QG.