Large \(N\) duality, Lagrangian cycles, and algebraic knots

DOI10.1007/s00220-012-1563-3zbMath1309.57011arXiv1111.6533OpenAlexW3101003725MaRDI QIDQ1950366

Cumrun Vafa, Vivek Shende, Duiliu-Emanuel Diaconescu

Publication date: 13 May 2013

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1111.6533

zbMATH Keywords

Lagrangian submanifoldtorus knotsChern-Simonsresolved conifoldopen Gromov-Witten invariantsHOMFLY polynomialsvirtual localizationconifold transitionS-matrix formula

Mathematics Subject Classification ID

String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Topological field theories in quantum mechanics (81T45)

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Remarks on Cohomological Hall Algebras and Their Representations, Stable pairs and the HOMFLY polynomial, Sequencing BPS spectra, 3d-3d correspondence revisited, The condensate from torus knots, Static charges in the low-energy theory of the S-duality twist, Topological recursion for the conifold transition of a torus knot, Lectures on knot homology, Torus knots and the topological vertex, On genus expansion of superpolynomials, New structures for colored HOMFLY-PT invariants, Fivebranes and 3-manifold homology, Refined large N duality for knots, Twisted spectral correspondence and torus knots, On the Gopakumar–Ooguri–Vafa correspondence for Clifford–Klein 3-manifolds, Stable maps to Looijenga pairs: orbifold examples, Torus knots in lens spaces and topological strings, Legendrian knots and constructible sheaves, BPS states, torus links and wild character varieties, Knot invariants from topological recursion on augmentation varieties, On BPS strings in \(\mathcal{N} = 4\) Yang-Mills theory, On explicit formulae of LMOV invariants, Knots, BPS states, and algebraic curves, A support theorem for Hilbert schemes of planar curves, II, A string dual for partially topological Chern-Simons-matter theories, Open Gromov-Witten invariants from the augmentation polynomial, A note on colored HOMFLY polynomials for hyperbolic knots from WZW models

Cites Work

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• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• New structures of knot invariants
• Wall crossing and M-theory
• Proof of the Labastida-Mariño-Ooguri-Vafa conjecture
• Chern-Simons invariants of torus links
• \(N=1\) mirror symmetry and open/closed string duality
• Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
• Lagrangians for the Gopakumar-Vafa conjecture
• Curve counting via stable pairs in the derived category
• Quantum field theory and the Jones polynomial
• Topological gravity as large \(N\) topological gauge theory
• The Alexander polynomial of a plane curve singularity via the ring of functions on it
• Torus knots and mirror symmetry
• String and vortex
• Symplectic conifold transitions.
• Disc instantons in linear sigma models
• Hodge integrals and invariants of the unknot
• A proof of a conjecture of Mariño-Vafa on Hodge integrals
• All loop topological string amplitudes from Chern-Simons theory
• Mirror symmetry is \(T\)-duality
• On a proof of the Labastida-Mariño-Ooguri-Vafa conjecture
• Conormal bundles to knots and the Gopakumar-Vafa conjecture
• Large \(N\)-duality for compact Calabi-Yau threefolds
• The topological vertex
• Localization and gluing of topological amplitudes
• A formula of two-partition Hodge integrals
• Stable pairs and BPS invariants
• Knots, links and branes at large \(N\)
• On the gauge theory/geometry correspondence
• M-theory, topological strings and spinning black holes
• Knot invariants and topological strings.