Perturbative/Non-Perturbative Aspects of Topological String Theory and Condensed Matter Physics

Abstract

Recently some novel relations between topological strings on some toric Calabi-Yau threefolds and Bloch electrons moving in two-dimensional lattices under uniform magnetic flux was found. It turns out that the modular double duality plays an important role. We compute the density of states of the condensed matter side and show that it matches with the imaginary part of the derivative of quantum A-period. We will analyze the bandwidths in great detail and show that it is related to the quantum B-period of the topological string side.