Framed knots at large N

Abstract

We study the framing dependence of the Wilson loop observable of U(N) Chern-Simons gauge theory at large N. Using proposed geometrical large N dual, this leads to a direct computation of certain topological string amplitudes in a closed form. This yields new formulae for intersection numbers of cohomology classes on moduli of Riemann surfaces with punctures (including all the amplitudes of pure topological gravity in two dimensions). The reinterpretation of these computations in terms of BPS degeneracies of domain walls leads to novel integrality predictions for these amplitudes. Moreover we find evidence that large N dualities are more naturally formulated in the context of U(N) gauge theories rather than SU(N).

26 pages, harvmac

References in corpus (4)

• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Disk Instantons, Mirror Symmetry and the Duality Web
• Virasoro constraints and the Chern classes of the Hodge bundle
• On Link Invariants and Topological String Amplitudes

Cited by in corpus (75)

• Generalized Global Symmetries
• Vortex Counting and Lagrangian 3-manifolds
• Worldsheet Derivation of a Large N Duality
• Open string amplitudes and large order behavior in topological string theory
• D-brane Charges in Five-brane backgrounds
• Chern-Simons Theory and Topological Strings
• Torus knots and mirror symmetry
• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Hodge integrals and invariants of the unknot
• Link Homologies and the Refined Topological Vertex
• On N=1 Mirror Symmetry for Open Type II Strings
• Large N Duality, Mirror Symmetry, and a Q-deformed A-polynomial for Knots
• Localization and Gluing of Topological Amplitudes
• ABJM Wilson Loops in Arbitrary Representations
• BPS Wall Crossing and Topological Strings
• Topological Open String Amplitudes On Orientifolds
• Phase transitions, double-scaling limit, and topological strings
• Level-rank duality of the U(N) WZW model, Chern-Simons theory, and 2d qYM theory
• Knot polynomials in the first non-symmetric representation
• Changing the preferred direction of the refined topological vertex
• String theory and the Kauffman polynomial
• Hurwitz numbers, matrix models and enumerative geometry
• Crepant resolutions and open strings
• Disc Instantons in Linear Sigma Models
• Localizations on Moduli Spaces and Free Field Realizations of Feynman Rules
• On the Worldsheet Derivation of Large N Dualities for the Superstring
• SU(N) quantum Racah coefficients & non-torus links
• Open topological strings and integrable hierarchies: Remodeling the A-model
• On genus expansion of superpolynomials
• Reformulated invariants for non-torus knots and links
• Summing up Open String Instantons and N=1 String Amplitudes
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
• Stable maps to Looijenga pairs
• Fractional Volterra Hierarchy
• U(N) Framed Links, Three-Manifold Invariants, and Topological Strings
• Non-compact Topological Branes on Conifold
• Macdonald topological vertices and brane condensates
• Distinguishing Mutant Knots
• Checks of integrality properties in topological strings
• A note on multiply wound BPS Wilson loops in ABJM
• Formulae of one-partition and two-partition Hodge integrals
• Integrality structures in topological strings I: framed unknot
• Colored HOMFLY polynomials from Chern-Simons theory
• Refined large N duality for knots
• SO(N) Reformulated Link Invariants from Topological Strings
• Composite Representation Invariants and Unoriented Topological String Amplitudes
• Toric Geometry and String Theory
• Composite Invariants and Unoriented Topological String Amplitudes
• Hodge-GUE correspondence and the discrete KdV equation
• Phase Space Distribution for Two-Gap Solution in Unitary Matrix Model
• Frame ambiguity in Open Gromov-Witten invariants
• A note on the topological order of noncommutative Hall fluids
• Worldsheet Interpretation of the Level-Rank Duality
• Large N dualities and transitions in geometry
• Knot Categorification from Mirror Symmetry, Part I: Coherent Sheaves
• Stable maps to Looijenga pairs: orbifold examples
• Topological strings, quiver varieties and Rogers-Ramanujan identities
• Grothendieck's Dessins d'Enfants in a Web of Dualities. II
• The local Donaldson-Thomas theory of curves
• HOMFLY polynomials, stable pairs and motivic Donaldson-Thomas invariants
• Lectures on the ELSV formula
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• Cubic Hodge integrals and integrable hierarchies of Volterra type
• Geometric Transitions, del Pezzo Surfaces and Open String Instantons
• Topological Rényi and Entanglement Entropy for a 2d q-deformed $U(N)$ Yang-Mills theory and its Chern-Simons dual
• Computations on B-model geometric transitions
• On a deformed topological vertex
• Integrable structures of specialized hypergeometric tau functions
• The Hodge-FVH Correspondence
• Large N Duality for Compact Calabi-Yau Threefolds
• On cubic Hodge integrals and random matrices
• Gromov-Witten invariants of toric Calabi-Yau threefolds
• Geometric Transitions and Open String Instantons
• The open string McKay correspondence for type A singularities
• A Gamma Class Formula for Open Gromov-Witten Calculations