Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings

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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), 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, ... continued below

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Aganagic, Mina; Ooguri, Hirosi; Saulina, Natalia & Vafa, Cumrun January 28, 2005.

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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), 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 sub-leading 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.

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  • Journal Name: Nuclear Physics B; Related Information: Journal Publication Date: 17 March 2005

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  • Report No.: LBNL-56688
  • Grant Number: DE-AC02-05CH11231
  • DOI: 10.1016/j.nuclphysb.2005.02.035 | External Link
  • Office of Scientific & Technical Information Report Number: 964004
  • Archival Resource Key: ark:/67531/metadc927490

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  • January 28, 2005

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  • Nov. 13, 2016, 7:26 p.m.

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  • Nov. 18, 2016, 2:26 p.m.

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Aganagic, Mina; Ooguri, Hirosi; Saulina, Natalia & Vafa, Cumrun. Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings, article, January 28, 2005; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc927490/: accessed June 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.