Non-perturbative Topological Strings from M-theory

Topological strings are simplified versions of full string theories. Like all string theories, they admit a perturbative genus expansion in their coupling. In this talk, I will describe a new approach to go beyond this expansion and gain exact full non-perturbative information on their partition function. The approach utilizes an identification between the topological string free energy and certain F-terms in the effective action of full type IIA strings. The latter are known to be calculable in a perturbative approach by uplifting IIA to M-theory and integrating out M2 branes. This is the famous calculation of Gopakumar and Vafa. I will describe recent results which show that integrating out the M2 branes infact yields not only the perturbative (asymptotic) expansion but the full exact non-perturbative free energy. The resulting expression manifests features expected from an exact expression, such as certain strong-weak coupling dualities, and special behaviour at self-dual values of the coupling.