Torus knots and mirror symmetry

DOI10.1007/s00023-012-0171-2zbMath1256.81086arXiv1105.2012OpenAlexW2007743955MaRDI QIDQ1762491

Andrea Brini, Marcos Mariño, Bertrand Eynard

Publication date: 27 November 2012

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.2012

Mathematics Subject Classification ID

String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Mirror symmetry (algebro-geometric aspects) (14J33)

Related Items

Blobbed topological recursion ⋮ Colored Kauffman homology and super-A-polynomials ⋮ BPS states in the \(\Omega\)-background and torus knots ⋮ Towards \(\mathcal{R}\)-matrix construction of Khovanov-Rozansky polynomials I. Primary \(T\)-deformation of HOMFLY ⋮ Multiplicity-free \(U_q(sl_N)\) 6-j symbols: relations, asymptotics, symmetries ⋮ Introduction to Khovanov homologies. I. Unreduced Jones superpolynomial ⋮ Think globally, compute locally ⋮ Superpolynomials for torus knots from evolution induced by cut-and-join operators ⋮ Factorization of differential expansion for antiparallel double-braid knots ⋮ On universal knot polynomials ⋮ Sequencing BPS spectra ⋮ Explicit examples of DIM constraints for network matrix models ⋮ A note on multiply wound BPS Wilson loops in ABJM ⋮ Colored HOMFLY polynomials for the pretzel knots and links ⋮ The condensate from torus knots ⋮ Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots? ⋮ Interplay between Macdonald and Hall-Littlewood expansions of extended torus superpolynomials ⋮ Entanglement entropy and the colored Jones polynomial ⋮ Toward \(\mathrm {U}(N|M)\) knot invariant from ABJM theory ⋮ Semiclassical limit of topological Rényi entropy in \(3d\) Chern-Simons theory ⋮ A new symmetry of the colored Alexander polynomial ⋮ Topological recursion for the conifold transition of a torus knot ⋮ Quantum curves from refined topological recursion: the genus 0 case ⋮ Lectures on knot homology ⋮ Torus knots and the topological vertex ⋮ Formal multidimensional integrals, stuffed maps, and topological recursion ⋮ Blobbed topological recursion: properties and applications ⋮ Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux ⋮ Checks of integrality properties in topological strings ⋮ Tabulating knot polynomials for arborescent knots ⋮ Matrix model and dimensions at hypercube vertices ⋮ Large \(N\) duality, Lagrangian cycles, and algebraic knots ⋮ A generalized topological recursion for arbitrary ramification ⋮ Genus expansion of HOMFLY polynomials ⋮ Cabling procedure for the colored HOMFLY polynomials ⋮ Distinguishing mutant knots ⋮ On the Gopakumar–Ooguri–Vafa correspondence for Clifford–Klein 3-manifolds ⋮ Torus knot polynomials and Susy Wilson loops ⋮ Stable maps to Looijenga pairs: orbifold examples ⋮ Perturbative analysis of the colored Alexander polynomial and KP soliton \(\tau\)-functions ⋮ COLORED HOMFLY POLYNOMIALS FROM CHERN–SIMONS THEORY ⋮ Harer-Zagier formulas for knot matrix models ⋮ Torus knots in lens spaces and topological strings ⋮ Root systems, spectral curves, and analysis of a Chern-Simons matrix model for Seifert fibered spaces ⋮ Quantum curves for Hitchin fibrations and the Eynard-Orantin theory ⋮ Knot invariants from topological recursion on augmentation varieties ⋮ A matrix model for the latitude Wilson loop in ABJM theory ⋮ Sum rules for characters from character-preservation property of matrix models ⋮ Knots, links, and long-range magic ⋮ Topological recursion in the Ramond sector ⋮ Quantum Racah matrices and 3-strand braids in representation \([3,3\)] ⋮ Condensates and instanton - torus knot duality. Hidden Physics at UV scale ⋮ Comments on knotted 1/2 BPS Wilson loops ⋮ HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations ⋮ Knot homology and refined Chern-Simons index ⋮ Tangle blocks in the theory of link invariants ⋮ Knots, BPS states, and algebraic curves ⋮ Exact SUSY Wilson loops on \(S^3\) from \(q\)-Virasoro constraints ⋮ A string dual for partially topological Chern-Simons-matter theories ⋮ \(\mathcal{N}=1\) super topological recursion ⋮ Multi-boundary entanglement in Chern-Simons theory with finite gauge groups ⋮ The Laplace Transform, Mirror Symmetry, and the Topological Recursion of Eynard–Orantin ⋮ Open Gromov-Witten invariants from the augmentation polynomial ⋮ Character expansion for HOMFLY polynomials. II. Fundamental representation. Up to five strands in braid ⋮ All order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials ⋮ On refined Chern-Simons and refined ABJ matrix models ⋮ A note on colored HOMFLY polynomials for hyperbolic knots from WZW models ⋮ Intersecting defects and supergroup gauge theory

Cites Work

• Unnamed Item
• Unnamed Item
• Localization for Wilson loops in Chern-Simons theory
• Topological expansion of the \(\beta\)-ensemble model and quantum algebraic geometry in the sectorwise approach
• The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
• Open topological strings and integrable hierarchies: remodeling the A-model
• Cohomological localization of Chern-Simons theory
• Chern-Simons invariants of torus links
• Open orbifold Gromov-Witten invariants of \({[\mathbb{C}^3/\mathbb{Z}_n}\): Localization and mirror symmetry]
• Enumerative geometry of stable maps with Lagrangian boundary conditions and multiple covers of the disc
• Lagrangians for the Gopakumar-Vafa conjecture
• Remodeling the B-model
• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• Geometric quantization of Chern-Simons gauge theory
• Invariants of algebraic curves and topological expansion
• Hecke algebra representations of braid groups and link polynomials
• Quantum field theory and the Jones polynomial
• Periodic knots and the skein polynomial
• Quantum geometry of refined topological strings
• Witten-Reshetikhin-Turaev invariants of Seifert manifolds
• Three-dimensional Chern-Simons theory as a theory of knots and links. III: Compact semi-simple group
• A proof of the full Mariño-Vafa conjecture
• Khovanov-Rozansky homology and topological strings
• The vertex on a strip
• Conormal bundles to knots and the Gopakumar-Vafa conjecture
• Mirror symmetry and supermanifolds
• Non-abelian localization for Chern-Simons theory
• Large \(N\)-duality for compact Calabi-Yau threefolds
• The topological vertex
• THE HOMFLY POLYNOMIAL FOR TORUS LINKS FROM CHERN–SIMONS GAUGE THEORY
• 𝑞,𝑡-Catalan numbers and knot homology
• Chern-Simons theory, the 1/N expansion, and string theory
• On the Hecke algebras and the colored HOMFLY polynomial
• The Superpolynomial for Knot Homologies
• Chern-Simons matrix models and Stieltjes-Wigert polynomials
• Geometrical relations and plethysms in the Homfly skein of the annulus
• Schur polynomials and biorthogonal random matrix ensembles
• ON THE INVARIANTS OF TORUS KNOTS DERIVED FROM QUANTUM GROUPS
• Topological expansion of mixed correlations in the Hermitian 2-matrix model andx–ysymmetry of theF_galgebraic invariants
• Disk Instantons, Mirror Symmetry and the Duality Web
• SOFT MATRIX MODELS AND CHERN–SIMONS PARTITION FUNCTIONS
• Knots, links and branes at large \(N\)
• On the gauge theory/geometry correspondence
• Knot invariants and topological strings.