A bstract Various observables in compact CFTs are required to obey positivity, discreteness, and integrality. Positivity forms the crux of conformal bootstrap, but understanding abstract implications discreteness integrality for space is lacking. We systematically study these constraints two-dimensional, non-holomorphic CFTs, making use two main mathematical results. First, we prove a theorem c...

It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. The Pfaffian state is related to the 2D Ising model and possesses fractionally charged excitations which are predicted to obey n...