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Research Frontiers in Conformal Field Theory Classification

Develops complete classifications of two-dimensional conformal field theories using operator algebra and modular properties.

Modular Invariance and Hidden Symmetries in CFT Partition Functions
Operator Product Expansion Singularities Beyond the Conformal Bootstrap
Defect Lines and Non-Local Operators in Higher-Dimensional Conformal Theories
Conformal Anomalies and Weyl Invariance in Curved Spacetime CFTs
Integrable Structures in Two-Dimensional Conformal Field Theories
Non-Rational CFTs and Continuous Operator Dimension Spectra
Conformal Interfaces and Boundary Entropy in Classification Schemes
Categorical Structures Underlying Conformal Field Theory Dualities
Fractional Conformal Dimensions and Logarithmic Operators in CFT
Superconformal Symmetry and its Extensions in Critical Phenomena

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