Solving Quantum Integrable Systems by Topological Strings

Abstract

It is known that topological string theory is related to integrable systems. This fact allows us to solve an integrable system by using results in the corresponding topological string. We show that the eigenvalue problem for a class of quantum integrable systems, including the relativistic Toda lattice, is indeed solved by the topological strings. It turns out that the obtained quantization conditions have a non-trivial strong-weak duality with respect to the Planck constant.