Two Dimensional Yang-Mills, Black Holes and Topological Strings

By C. Vafa. 2004

133 citations recorded by the source corpus.

We show that topological strings on a class of non-compact Calabi-Yau threefolds is equivalent to two dimensional bosonic U(N) Yang-Mills on a torus. We explain this correspondence using the recent results on the equivalence of the partition function of topological strings and that of four dimensional BPS black holes, which in turn is holographically dual to the field theory on a brane. The partition function of the field theory on the brane reduces, for the ground state sector, to that of 2d Yang-Mills theory. We conjecture that the large N chiral factorization of the 2d U(N) Yang-Mills partition function reflects the existence of two boundaries of the classical AdS_2 geometry, with one chiral sector associated to each boundary; moreover the lack of factorization at finite N is related to the transformation of the vacuum state of black hole from a pure state at all orders in 1/N to a state which appears mixed at finite N (due to O(e^{-N}) effects).

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e3fb66abd52d75feff7499644ba41c79c1d88f18

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. B. Pioline
2. Ashoke Sen
3. G. Moore
4. C. Vafa
5. Frederik Denef
6. Hirosi Ooguri
7. A. Klemm
8. Mina Aganagic

In Nuclear and High Energy Physics

1. C. Vafa
2. Marcos Mariño
3. Ashoke Sen
4. A. Klemm
5. B. Pioline
6. Sergei Gukov
7. Mina Aganagic
8. Min-xin Huang

In Statistical and Nonlinear Physics

1. C. Vafa
2. Marcos Mariño
3. B. Pioline
4. Ashoke Sen
5. A. Klemm
6. G. Moore
7. Mina Aganagic
8. Min-xin Huang

Citations in the corpus

• Hartle–Hawking Wave-Function for Flux Compactifications: the Entropic Principle (2005, methodology): “We will identify physical degrees of freedom for this extra factor and how it combines with the complex structure moduli and described by the action (2.11).”
• Black hole partition functions and duality (2006, unknown): “Further work in that direction can be found in [ 10 , 11, 12, 13], where the conjecture was tested for the case of non-compact Calabi-Yau spaces.”
• Exact and Asymptotic Degeneracies of Small Black Holes (2005, unknown): “1) have previously been addressed in [59][60].”
• Electric/magnetic deformations of S3 and AdS3, and geometric cosets (2004, unknown): “an interesting candidate for AdS/cftcorrespondence [42]. In the present case the dual theory should correspond to some superconformal quantum mechanics [5, 43, 44, 45]. According to some recent works [46, 47], these string theory black holes are deeply related to topological strings on the Calabi-Ya”
• 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].”
• Topological String Theory on Compact Calabi–Yau: Modularity and Boundary Conditions (2006, background): “- [1] or large N-techniques [2] and has intriguing connections to Chern-Simons theory [3], open-closed string duality [4], matrix models [5], integrable hierarchies of non-critical string theory [6] and 2d Yang-Mills theory [7].”
• Topological M-theory as unification of form theories of gravity (2004, background): “Moreover, their nonperturbative definition has begun to emerge through their deep connection with the counting of BPS black hole states in 4 dimensions [5,6].”
• Supersymmetric Gauge Theories, Intersecting Branes and Free Fermions (2007, methodology): “) The latter has a description in toric geometry as glueing the toric propagator to itself with a framing factor r. This changes the intersection of [T2] with the 4-cycles that project onto T2 into ±r[65]. In this section we show how one can use the picture we 46 have developed in this paper, and in”
• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings (2004, methodology): “Moreover there is an extra sum over integers: This extra sum has been explained in [2] as being related to summing over RR fluxes in the geometry (or alternatively it is required for making the chemical potential has suitable periodicity in the imaginary direction).”
• 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 ”