Holomorphic Factorization Research Articles

Determinants, torsion, and strings

We apply the results of [BF1, BF2] on determinants of Dirac operators to String Theory. For the bosonic string we recover the “holomorphic factorization” of Belavin and Knizhik. Witten's global anomaly formula is used to give sufficient conditions for anomaly cancellation in the heterotic string (for arbitrary background spacetimes). To prove the latter result we develop certain torsion invariants related to characteristic classes of vector bundles and to index theory.

A note on holomorphic matric automorphic factors with respect to a lattice in a complex vector space

A holomorphic n × n-matric automorphic factor with respect to a lattice L in Cg means a system of holomorphic n × n-matrices {μα(z) | α ∈ L} such that