  We study general perturbations of two-dimensional conformal field theories by
holomorphic fields. It is shown that the genus one partition function is
controlled by a contact term (pre-Lie) algebra given in terms of the operator
product expansion. These models have applications to vertex operator algebras,
two-dimensional QCD, topological strings, holomorphic anomaly equations and
modular properties of generalized characters of chiral algebras such as the
$W_{1+\infty}$ algebra, that is treated in detail.

High Energy Physics - Theory