Polynomial Invariants for Torus Knots¶and Topological Strings
By J. Labastida, Marcos Mariño. 2000
165 citations recorded by the source corpus.
Abstract: 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.
Subfields: Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/83372c166ff968d091a5c902b36bdc8827670689
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Citations in the corpus
- Mirror symmetry, D-branes and counting holomorphic discs (2000, methodology): “Using the large N duality conjecture [12] there have been some cases where one can compute certain corrections involving holomorphic maps from Riemann surfaces with boundaries to target space geometry [6][13][14].”
- The Topological Vertex (2003, methodology): “Various aspects of this duality have been studied in [22,31,32,33], in particular in [22] the duality was studied in the presence of non-compact D-branes.”
- Fivebranes and Knots (2011, background): “For further developments see [76], [87], and [75]; for a review of many of these topics see [78].”
- On the Hecke algebras and the colored HOMFLY polynomial (2006, methodology): “A formula of the colored HOMFLY polynomial for torus knots is given in [10], which was used to test the Labastida-Mari˜no-Vafa conjecture on torus knots.”
- Worldsheet derivation of a large N duality (2002, background): “Many checks have been performed for this conjectured duality including highly nontrivial tests involving Wilson loop operators to all order in the gauge coupling constant [8,9,10,11].”
- Chern-Simons theory and topological strings (2004, unknown): “C (Labastida and Mariño, 2001; Ramadevi and Sharkar, 2001; Labastida, Mariño, and Vafa, 2000; Labastida and Mariño, 2002; Mariño, 2002b).”
- Khovanov-Rozansky Homology and Topological Strings (2004, methodology): “These conventions are compatible with the ones used in [14,15,16,17,18], but differ from the conventions used in the physics literature [5,6,7,8,23,24].”
- Knots, links and branes at large N (2000, background): “The results of [3] strongly suggest that for non-trivial torus knots, the integer invariants NR,Q,s are non-vanishing for all representations.”
- Knot Homology from Refined Chern-Simons Theory (2011, background): “Many checks of this were performed in [10][11].”
- Partition functions of holographic minimal models (2011, methodology): “2) is similar to the Ooguri-Vafa operator [33] (see also [34, 35, 36]) that arises in the topological string computation of knot invariants.”
- All Loop Topological String Amplitudes from Chern-Simons Theory (2002, methodology): “Before we proceed, it is key to note that there is an illuminating way to write the operator O(U1, U2; r), by using the techniques of [3].”
- Disk Instantons, Mirror Symmetry and the Duality Web (2001, methodology): “To see how this works it is simplest to consider the case where the D-brane topological amplitudes were computed using the observables of Chern-Simons theory [4][27][26].”