Exact eigenfunctions and the open topological string

Understand

Mirror curves to toric Calabi-Yau threefolds can be quantized and lead to trace class operators on the real line.

• The eigenvalues of these operators are encoded in the BPS invariants of the underlying threefold, but much less is known about their eigenfunctions.
• In this paper we first develop methods in spectral theory to compute these eigenfunctions.
• We also provide a matrix integral representation which allows to study them in a 't Hooft limit, where they are described by standard topological open string amplitudes.