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Checks of integrality properties in topological strings

  • A. MironovEmail author
  • A. Morozov
  • An. Morozov
  • P. Ramadevi
  • Vivek Kumar Singh
  • A. Sleptsov
Open Access
Regular Article - Theoretical Physics

Abstract

Tests of the integrality properties of a scalar operator in topological strings on a resolved conifold background or orientifold of conifold backgrounds have been performed for arborescent knots and some non-arborescent knots. The recent results on polynomials for those knots colored by SU(N ) and SO(N ) adjoint representations [1] are useful to verify Marino’s integrality conjecture up to two boxes in the Young diagram. In this paper, we review the salient aspects of the integrality properties and tabulate explicitly for an arborescent knot and a link. In our knotebook website, we have put these results for over 100 prime knots available in Rolfsen table and some links. The first application of the obtained results, an observation of the Gaussian distribution of the LMOV invariants is also reported.

Keywords

Chern-Simons Theories Topological Strings 

Notes

Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • A. Mironov
    • 1
    • 2
    • 3
    • 6
    Email author
  • A. Morozov
    • 2
    • 3
    • 6
  • An. Morozov
    • 2
    • 3
    • 4
    • 6
  • P. Ramadevi
    • 5
  • Vivek Kumar Singh
    • 5
  • A. Sleptsov
    • 2
    • 3
    • 4
    • 6
  1. 1.Theory DepartmentLebedev Physics InstituteMoscowRussia
  2. 2.ITEPMoscowRussia
  3. 3.Institute for Information Transmission ProblemsMoscowRussia
  4. 4.Laboratory of Quantum TopologyChelyabinsk State UniversityChelyabinskRussia
  5. 5.Department of PhysicsIndian Institute of Technology BombayMumbaiIndia
  6. 6.National Research Nuclear University MEPhIMoscowRussia

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