D-branes and D-modules

We study of chiral fermions on a quantum curve by embedding them in string theory as an intersecting D-brane configuration together with a B-field. Mathematically, this system is described by a holonomic D-module. Here we focus on spectral curves, which play a prominant role in the theory of (quantum) integrable hierarchies. We show how to associate a quanfum state to the system, and subsequently how to compute quantum invariants. The material of this paper is treated at greater length in the paper that also contains many examples. (author)