Aganagic, MinaOoguri, HirosiSaulina, NataliaVafa, Cumrun2019-09-222005Aganagic, Mina, Hirosi Ooguri, Natalia Saulina, and Cumrun Vafa. 2005. “Black Holes, Q-Deformed 2d Yang–Mills, and Non-Perturbative Topological Strings.” Nuclear Physics B 715 (1–2): 304–48. https://doi.org/10.1016/j.nuclphysb.2005.02.035.0169-68230550-32131873-1562http://nrs.harvard.edu/urn-3:HUL.InstRepos:41385090We count the number of bound states of BPS black holes on local Calabi-Yau three-folds involving a Riemann surface of genus g. We show that the corresponding gauge theory on the brane reduces to a q-deformed Yang-Mills theory on the Riemann surface. Following the recent connection between the black hole entropy and the topological string partition function, we find that for a large black hole charge N, up to corrections of O(e(-N)), Z(BH) is given as a sum of a square of chiral blocks, each of which corresponds to a specific D-brane amplitude. The leading chiral block, the vacuum block, corresponds to the closed topological string amplitudes. The subleading chiral blocks involve topological string amplitudes with D-brane insertions at (2g - 2) points on the Riemann surface analogous to the Omega points in the large N 2d Yang-Mills theory. The finite N amplitude provides a non-perturbative definition of topological strings in these backgrounds. This also leads to a novel non-perturbative formulation of c = 1 non-critical string at the self-dual radius.en-USJournal Article2019-09-2210.1016/j.nuclphysb.2005.02.035