Geometry of superconformal field theories in two dimensions (Q578670)

An infinitesimal superconformal transformation of a domain in a (1,1)- dimensional complex superspace with coordinates (z,\(\theta)\) is defined by \({\tilde \partial}z=u(z)-\epsilon (z)\theta\) and \(\delta \theta =\epsilon (z)+u'(z)\theta\), where u and \(\epsilon\) are even and odd analytic functions of z, respectively. Any manifold glued from (1,1)- dimensional superdomains with the help of superconformal mappings is called a superconformal manifold of dimension (1,1). The space of equivalence classes of such manifolds is studied and its connection with a fermionic string in the critical dimension is pointed out.