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Explore a detailed physics lecture that delves into a systematic approach for relating continuum Quantum Field Theory (QFT) to lattice QFT using higher categories and higher anafunctors. Learn how topological operators from continuum theory can be naturally defined on the lattice, addressing the long-standing challenge of defining instanton and Chern-Simons terms in lattice Yang-Mills theory. Discover how this formalism effectively captures the interpolation possibilities between lattice fields and the continuum, naturally incorporating higher categories from homotopy theory. Understand how this approach, when applied to discrete-valued fields, reduces to Dijkgraaf-Witten theory and Turaev-Viro theory, potentially offering a pathway toward a comprehensive categorical understanding of QFT that encompasses both continuous and discrete degrees of freedom, applicable to both infrared and ultraviolet physics.
