Titill fyrirlestrar: Non-chiral current algebras in conformal field theory

Útdráttur:

Vertex operator algebras arise in two-dimensional conformal quantum field theories (CFT's) in connection with symmetries. In a quantum field theory whose symmetry is a Lie group G one expects to have currents which are vector quantum fields carrying the adjoint representation of the Lie algeba of G and satisfying the null divergence equation (conservation equation). In unitary CFT's such currents are holomorphic (or anti-holomorphic fields). For example in Wess-Zumino-Witten CFT's the symmetry group is two copies of a Lie group G that is GxG, the corresponding currents are either holomorphic or anti-holomorphic and their Laurant modes satisfy a Kac-Moody algebra commutation relations. I will consider examples of non-unitary CFT's in which the currents do not split into holomorphic/antiholomorphic components. These examples lead to local operator algebras of a more complicated structure than that of vertex operator algebras. I will report on attempts to uncover this structure.