Aganagic, Mina and Ooguri, Hirosi and Saulina, Natalia and Vafa, Cumrun
(2005)
*Black holes, q-deformed 2d Yang-Mills, and non-perturbative topological strings.*
Nuclear Physics B, 715
(1-2).
pp. 304-348.
ISSN 0550-3213.
http://resolver.caltech.edu/CaltechAUTHORS:20110513-093141123

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## Abstract

We 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)), ZBH 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 Ω 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.

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Additional Information: | © 2005 Elsevier B.V. Received 28 January 2005; accepted 23 February 2005. Available online 17 March 2005. This article is registered under preprint number hep-th/0411280. We are grateful to C. Beasley, J. Bryan, M. Marino, A. Neitzke and R. Pandharipande W. Taylor and E. Witten for valuable discussions. H.O. and C.V. thank the 2004 Simons Workshop on mathematics and physics, for stimulating talks. H.O. in addition thanks the Aspen Center for Physics and the High Energy Theory Group at Harvard University for their hospitalities. The research of M.A. was supported in part by a DOE OJI Award, and an Alfred P. Sloan Foundation fellowship. The research of H.O. was supported in part by DOE grant DE-FG03-92-ER40701. The research of N.S. and C.V. was supported in part by NSF grants PHY-0244821 and DMS-0244464. | ||||||||||||

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Record Number: | CaltechAUTHORS:20110513-093141123 | ||||||||||||

Persistent URL: | http://resolver.caltech.edu/CaltechAUTHORS:20110513-093141123 | ||||||||||||

Official Citation: | Mina Aganagic, Hirosi Ooguri, Natalia Saulina, Cumrun Vafa, Black holes, q-deformed 2d Yang-Mills, and non-perturbative topological strings, Nuclear Physics B, Volume 715, Issues 1-2, 23 May 2005, Pages 304-348, ISSN 0550-3213, DOI: 10.1016/j.nuclphysb.2005.02.035. | ||||||||||||

Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||

ID Code: | 23658 | ||||||||||||

Collection: | CaltechAUTHORS | ||||||||||||

Deposited By: | Ruth Sustaita | ||||||||||||

Deposited On: | 17 May 2011 18:40 | ||||||||||||

Last Modified: | 17 Dec 2016 00:02 |

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