Communications in Mathematical Physics

, Volume 217, Issue 2, pp 423–449

Polynomial Invariants for Torus Knots¶and Topological Strings

  • J. M. F. Labastida
  • Marcos Mariño

DOI: 10.1007/s002200100374

Cite this article as:
Labastida, J. & Mariño, . Commun. Math. Phys. (2001) 217: 423. doi:10.1007/s002200100374


We make a precision test of a recently proposed conjecture relating Chern–Simons gauge theory to topological string theory on the resolution of the conifold. First, we develop a systematic procedure to extract string amplitudes from vacuum expectation values (vevs) of Wilson loops in Chern–Simons gauge theory, and then we evaluate these vevs in arbitrary irreducible representations of SU(N) for torus knots. We find complete agreement with the predictions derived from the target space interpretation of the string amplitudes. We also show that the structure of the free energy of topological open string theory gives further constraints on the Chern–Simons vevs. Our work provides strong evidence towards an interpretation of knot polynomial invariants as generating functions associated to enumerative problems.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • J. M. F. Labastida
    • 1
  • Marcos Mariño
    • 2
  1. 1.Departamento de Física de Parículas, Universidade de Santiago de Compostela,¶15706 Santiago de Compostela, Spain. E-mail: labasti@fpaxp1.usc.esES
  2. 2.New High Energy Theory Center, Rutgers University, Piscataway, NJ 08855, USA.¶E-mail: marcosm@physics.rutgers.eduUS