Aganagic, MinaCheng, Miranda C. N.Dijkgraaf, RobbertKrefl, DanielVafa, Cumrun2019-09-222012Aganagic, Mina, Miranda C. N. Cheng, Robbert Dijkgraaf, Daniel Krefl, and Cumrun Vafa. 2012. “Quantum Geometry of Refined Topological Strings.” Journal of High Energy Physics 2012 (11). https://doi.org/10.1007/jhep11(2012)019.1029-84791126-6708http://nrs.harvard.edu/urn-3:HUL.InstRepos:41385027We consider branes in refined topological strings. We argue that their wavefunctions satisfy a Schrodinger equation depending on multiple times and prow this in the case where the topological string has a dual matrix model description. Furthermore, in the limit where one of the equivariant rotations approaches zero, the brane partition function satisfies a time-independent Schrodinger equation. We use this observation, as well as the back reaction of the brane on the closed string geometry, to offer an explanation of the connection between integrable systems and N = 2 gauge systems in four dimensions observed by Nekrasov and Shatashvili.en-USJournal Article2019-09-2210.1007/JHEP11(2012)019