Krichever-Novikov formulation of topological conformal field theory (Q1184557)

In the Krichever-Novikov global operator approach to conformal field theory on higher genus Riemann surfaces the (holomorphic parts of the) fields of weight \(\lambda\) are expanded with respect to a distinguished basis of the space of meromorphic sections with prescribed set of poles of the \(\lambda\)-tensor power of the canonical bundle. For example, the energy-momentum tensor is a form of weight two. Its operator valued expansion coefficients give a representation of a centrally extended Krichever-Novikov algebra (this algebra is a generalization of the Virasoro algebra to higher genus). The authors start from an \(N=2\) superconformal field theory in the Krichever-Novikov picture. They twist the whole operator content of the theory to obtain a topological conformal field theory on higher genus Riemann surfaces in such a way that the operator valued expansion coefficients of the energy-momentum tensor now fulfil a centerless Krichever-Novikov algebra. The operator content of this field theory is studied. In particular, the BRST- cohomology structure of the Hilbert space of the theory is examined.