Elliptic Genera, Transgression and Loop Space Chern-Simons Forms
  We compute the Chern-Simons transgressed forms of some modularly invariant characteristic forms, which are related to the elliptic genera. We study the modularity properties of these secondary characteristic forms and the relations among them. We also compute the Chern-Simons forms of some vector bundles over free loop space. 
Qingtao Chen and Fei Han