Modular Invariance and Selection Rules for RG Flows

Explore the fundamental principles of modular invariance and selection rules governing renormalization group (RG) flows in this 51-minute conference talk delivered as part of the Program on Anomalies, Topology and Quantum Information in Field Theory and Condensed Matter Physics. Delve into the mathematical framework that constrains how quantum field theories evolve under changes of energy scale, examining how modular transformations impose restrictions on possible RG flow trajectories. Learn about the deep connections between conformal field theory, modular invariance properties, and the selection rules that determine which RG flows are physically permissible. Discover how these theoretical tools provide powerful constraints for understanding phase transitions and critical phenomena in both high-energy physics and condensed matter systems. Gain insights into the interplay between topology, quantum information, and field theory through the lens of modular invariance, and understand how these concepts contribute to our broader understanding of quantum many-body systems and their universal properties.