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

By Mina Aganagic, Hirosi Ooguri, N. Saulina, C. Vafa. 2004

257 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/daf27691e0671395957125d80f162c30ad0cbec9

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Citations in the corpus

Knot Homology from Refined Chern-Simons Theory (2011, background): “A theory such as ours is in essence two dimensional, as all of its topological data can be phrased in terms of Σ [65,61].”
QUANTUM FIELD THEORIES (2004, background): “Recent discoveries of Vafa and his collaborators [ 37 ] clearly prove that q-deformation will play an important role in string theory, Yang-Mills theory and Black holes.”
Minimal model holography (2012, unknown): “ion of Λ, SΛ0 S00 = dimq(Λ) = P w∈W ǫ(w)q −hw(Λ+ˆρ),ρˆi P w∈W ǫ(w)q−hw(ˆρ),ρˆi . (155) (Here Sab are the matrix elements of the Smodular transformation matrix of the aﬃne algebra.) Using results from [2] and [72], one can show that the quantum dimension of Λ factorises as qC2(Λ) dim q(Λ) ∼= qC2(R) d”
Partition Functions of $${\mathcal{N}=(2,2)}$$N=(2,2) Gauge Theories on S2 and Vortices (2012, unknown): “As in [44] we can shift ni → ni+ N−α+1 2 − i, restrict the sum to ordered integers n1 ≥ · · · ≥ nN (because of the last factor in (5.”
Hartle–Hawking Wave-Function for Flux Compactifications: the Entropic Principle (2005, background): “perturbative expansion, as stressed in [19, 20 ].”
Exact and Asymptotic Degeneracies of Small Black Holes (2005, unknown): “1) have previously been addressed in [59][60].”
Precision Counting of Small Black Holes (2005, background): “]. One aim ofourwork is make Eqs. (1.7),(1.6)more precise and use themtostudy the degeneracies of ﬁnite charge black holes. Certain proposed nonperturbative corrections to (1.7) have been explored in [25,26], but in a rather diﬀerent context from the examples studied here. 1.2 Small Black Holes For ”
Lectures on black holes, topological strings and quantum attractors (2006, methodology): “Similar averaging have indeed been found to occur in some non-compact models [92, 93].”
On the superconformal index of Argyres–Douglas theories (2015, methodology): “This version is obtained by deforming g m ,  with one parameter q C Î [54] (we recover ordinary two-dimensional YM”
Non-Abelian localization for Chern-Simons theory (2005, unknown): “This two-dimensional interpretation of Chern-Simons theory on M has also been noted recently by Aganagic and collaborators in [14], where the theory is identified with a q-deformed version of two-dimensional Yang-Mills theory.”