From Continuum to the Lattice in Conformal Field Theory

Explore the mathematical transition from continuous to discrete formulations in conformal field theory through this seminar lecture delivered by Professor Ingo Runkel from Universität Hamburg at the Isaac Newton Institute. Delve into the fundamental concepts and techniques used to bridge continuum and lattice approaches in conformal field theory, examining how continuous field theories can be discretized while preserving essential conformal properties. Learn about the mathematical frameworks and methodologies that enable this transition, including the preservation of symmetries and the handling of boundary conditions in discrete settings. Understand the theoretical foundations that connect smooth manifold descriptions with lattice-based formulations, and discover how this transition impacts the study of quantum field theories with boundaries, impurities, and defects. Gain insights into advanced mathematical physics concepts through detailed explanations of the discretization process and its implications for conformal field theory applications.