Conformal Field Theory
Conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations — mappings that preserve angles but not necessarily lengths. In a CFT, the theory looks the same at all scales: zooming in or out does not change the physics. This property, called scale invariance, makes CFTs powerful tools for studying critical phenomena and phase transitions.
CFTs are deeply connected to string theory (worldsheet theories are CFTs), to the holographic principle (the AdS/CFT correspondence), and to statistical mechanics (critical points are described by CFTs). The algebraic structure of CFTs — in particular the representation theory of the Virasoro algebra and its extensions — has also enriched algebraic geometry and representation theory.