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Refined black hole ensembles and topological strings

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Abstract

We formulate a refined version of the Ooguri-Strominger-Vafa (OSV) conjecture. The OSV conjecture that Z BH = |Z top |2 relates the BPS black hole partition function to the topological string partition function Z top. In the refined conjecture, Z BH is the partition function of BPS black holes counted with spin, or more precisely the protected spin character. Z top becomes the partition function of the refined topological string, which is itself an index. Both the original and the refined conjecture are examples of large N duality in the ’t Hooft sense. The refined conjecture applies to non-compact Calabi-Yau manifolds only, so the black holes are really BPS particles with large entropy, of order N 2. The refined OSV conjecture states that the refined BPS partition function has a large N dual which is captured by the refined topological string. We provide evidence that the conjecture holds by studying local Calabi-Yau threefolds consisting of line bundles over a genus g Riemann surface. We show that the refined topological string partition function on these geometries is computed by a two-dimensional TQFT. We also study the refined black hole partition function arising from N D4 branes on the Calabi-Yau, and argue that it reduces to a (q, t)-deformed version of two-dimensional SU(N ) Yang-Mills. Finally, we show that in the large N limit this theory factorizes to the square of the refined topological string in accordance with the refined OSV conjecture.

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  1. Center for Theoretical Physics, University of California, Berkeley, CA, 94720, U.S.A.

    Mina Aganagic & Kevin Schaeffer

  2. Department of Mathematics, University of California, Berkeley, CA, 94720, U.S.A.

    Mina Aganagic

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  1. Mina Aganagic
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Correspondence to Mina Aganagic.

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ArXiv ePrint: 1210.1865

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Aganagic, M., Schaeffer, K. Refined black hole ensembles and topological strings. J. High Energ. Phys. 2013, 60 (2013). https://doi.org/10.1007/JHEP01(2013)060

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