Spectral Theory and Mirror Curves of Higher Genus

Understand

Recently, a correspondence has been proposed between spectral theory and topological strings on toric Calabi-Yau manifolds.

• In this paper we develop in detail this correspondence for mirror curves of higher genus, which display many new features as compared to the genus one case studied so far.
• Given a curve of genus g, our quantization scheme leads to g different trace class operators.
• Their spectral properties are encoded in a generalized spectral determinant, which is an entire function on the Calabi-Yau moduli space.