Conformality, Rationality, Modularity: A Character Drama

by Prof. Sunil Mukhi (IISER Pune)

Tuesday 15 Apr 2025, 16:00 → 17:00 Asia/Kolkata

AG (69)

I will survey how Conformal Field Theories in two dimensions are classified. The combined requirements of conformal symmetry, rational exponents and modular invariance permit the implementation of a powerful self-consistency condition ("bootstrap") which enables us to construct consistent characters for this drama. This, however, does not ensure their existence as genuine field theories. However, when coupled with mathematical studies on lattices and their generalisations, a far more powerful result is obtained: classifications of fully consistent, solvable conformal field theories with small numbers of critical exponents. This talk is designed for the complement of the String Theory community, so no prior knowledge beyond basic QFT will be assumed.