All Loop Topological String Amplitudes from Chern-Simons Theory

By Mina Aganagic, Marcos Mariño, C. Vafa. 2002

204 citations recorded by the source corpus.

We demonstrate the equivalence of all loop closed topological string amplitudes on toric local Calabi-Yau threefolds with computations of certain knot invariants for Chern-Simons theory. We use this equivalence to compute the topological string amplitudes in certain cases to very high degree and to all genera. In particular we explicitly compute the topological string amplitudes for 2 up to degree 12 and 1× 1 up to total degree 10 to all genera. This also leads to certain novel large N dualities in the context of ordinary superstrings, involving duals of type II superstrings on local Calabi-Yau three-folds without any fluxes.

Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/85204bb9e3610b826f62950fa7756f393f41f864

How researchers see this paper

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In Geometry and Topology

1. Marcos Mariño
2. C. Vafa
3. Sergei Gukov
4. A. Klemm
5. Mina Aganagic
6. Tudor Dimofte
7. V. Bouchard
8. Pavel Putrov

In Mathematical Physics

1. Marcos Mariño
2. C. Vafa
3. Mina Aganagic
4. Sergei Gukov
5. A. Klemm
6. B. Eynard
7. Tudor Dimofte
8. V. Bouchard

In Nuclear and High Energy Physics

1. Marcos Mariño
2. C. Vafa
3. A. Klemm
4. Mina Aganagic
5. Sergei Gukov
6. Yasuyuki Hatsuda
7. H. Kanno
8. Tudor Dimofte

Citations in the corpus

• Partition functions of holographic minimal models (2011, unknown): “Following [40] we have the identity T 0,0 TΛ+Λ+ SΛ+Λ− TΛ−Λ− = ∑”
• The Topological Vertex (2003, methodology): “In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.”
• Non-perturbative effects and the refined topological string (2013, background): “This can indeed be done by the topological vertex [35, 36] or by direct integration of the holomorphic anomaly equations [6, 37], for example.”
• Topological Strings and (Almost) Modular Forms (2006, background): “The Gromov-Witten theory of the local IP(2) at large radius was solved in [3,4] .”
• REFINED BPS STATE COUNTING FROM NEKRASOV'S FORMULA AND MACDONALD FUNCTIONS (2008, methodology): “We provide diagrammatic rules for computing the partition function from the web diagrams appearing in geometric engineering of Yang-Mills theory with eight supercharges.”
• Vortex Counting and Lagrangian 3-Manifolds (2010, background): “Additional Ooguri-Vafa factors would need to be introduced (at least in the unrefined limit q1 = q2) to account for interactions [41].”
• Knot Homology from Refined Chern-Simons Theory (2011, methodology): “We derive a matrix integral expression for the S matrix of the theory, refining the Chern-Simons matrix model of [26,27].”
• Matrix models, topological strings, and supersymmetric gauge theories (2002, methodology): “Embedding this kind of theory in type IIB strings gives exactly the kind of N → ∞ dualities proposed recently in [19] which relate certain limits of gauge systems with type IIB strings on Calabi-Yau geometries without fluxes.”
• Gravitational corrections in supersymmetric gauge theory and matrix models (2002, methodology): “We have calculated the Gromov-Witten invariants using the above procedure and found agreement with genus 2 results of [27], who used the same method and at higher genus with the ones evaluated in [28] using Chern-Simons theory.”
• Topological Strings and Integrable Hierarchies (2003, background): “where WR1R2 is the large N limit of the CS invariant of the Hopf link, as defined in [50,9], and WR = WR·, where · denotes the trivial representation, is the large N limit of the quantum dimension of R.”
• On geometry and matrix models (2002, methodology): “In this case the A-model has a gauge theory dual involving certain correlations functions of Chern-Simons theory [23,28].”
• Matrix model as a mirror of Chern-Simons theory (2002, methodology): “For example, the mirror of T ∗S3 in (3.1) is given by blowup of xy = (eu − 1)(ev − 1) as described above.”
• A mathematical theory of the topological vertex (2004, methodology): “Since Yi,j and Yi,j′ are connected to the same connected component Ei ⊂ X ([2]), ci,j i,j = c ki,j′ i,j′ ; we let it be ci.”
• Toda Theories, Matrix Models, Topological Strings, and N=2 Gauge Systems (2009, background): “It turns out that the simplest examples of such N = 2 CFT’s were already constructed in the type IIA setup in [17] as a precursor to the more general construction embodied in the topological vertex.”
• Instanton effects in ABJM theory from Fermi gas approach (2012, methodology): “The Gopakumar-Vafa invariants ng~ d of local F0 were computed in [28].”