We review some recent progress in computing massless spectra and moduli in heterotic string compactifications. In particular, it was recently shown that the heterotic Bianchi Identity can be accounted for by the construction of a holomorphic operator. Mathematically, this corresponds to a holomorphic double extension. Moduli can then be computed in terms of cohomologies of this operator. We will see how the same structure can be derived form a Gukov-Vafa-Witten type superpotential. We note a relation between the lifted complex structure and bundle moduli, and cover some examples, and briefly consider obstructions and Yukawa couplings arising from these structures.
- String Theory Seminar