A note on topological amplitudes in hybrid string theory
  We study four-dimensional compactifications of type II superstrings on Calabi-Yau spaces in the hybrid formalism. Chiral and twisted-chiral interactions are rederived, which involve the coupling of the compactification moduli to two powers of the Weyl-tensor and of the derivative of the universal tensor field-strength. We review the formalism and provide details of some of its technicalities. 
J. Kappeli, S. Theisen, P. Vanhove