The Mathematics of Conformal Field Theory

Conformal field theories are quantum field theories whose measurable quantities are invariant under conformal changes of coordinates, that is, coordinate transformations which preserve angles, but not necessarily lengths. It turns out that in 2 space-time dimensions there are infinitely many independent (local) conformal transformations. This means that 2 dimensional conformal field theories have infinitely many constraints coming from conformal symmetry. These infinite constraints are what make it possible to solve (some) conformal field theories exactly and allow one to avoid using approximations or mathematically ill defined notions such as path integrals.

Conformal invariance endows conformal field theories with a rich mathematical structure. This mathematical structure is what makes conformal field theory an active topic of mathematical research and exploring it will form the core of this project