The Homfly Polynomial of the Decorated Hopf Link

Morton, H. R.; Lukac, Sascha G.

doi:10.1142/s0218216503002536

Cited by 62 publications

(53 citation statements)

References 9 publications

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“…More details and examples can be found in [37]. It is easy to see from (7.11) that the leading power in λ of W R 1 ,R 2 is (ℓ 1 + ℓ 2 )/2, and its coefficient is given by the leading coefficient of the quantum dimension, (7.5), times a rational function of q ± 1 2 that is given by:…”

Section: And Where D(µ)mentioning

confidence: 99%

The Topological Vertex

Aganagic

Klemm

Mariño

et al. 2004

Commun. Math. Phys.

674

1,584

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We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact toric Calabi-Yau threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kähler classes of the threefold. We interpret this result as an operatorial computation of the amplitudes in the B-model mirror which is the quantum KodairaSpencer theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.

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Section: And Where D(µ)mentioning

confidence: 99%

The Topological Vertex

Aganagic

Klemm

Mariño

et al. 2004

Commun. Math. Phys.

674

1,584

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“…Morton and Lukac used this kind of specialization of Schur functions to express the quantum dimension and Hopf link invariants [13]. For example, when a = λ −1 , b = 1,…”

Section: Hopf Link Invariants and Specialization Of Schur Functionmentioning

confidence: 99%

Universal character and large N factorization in topological gauge/string theory

Kanno

2006

Nuclear Physics B

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We establish a formula of the large N factorization of the modular S-matrix for the coupled representations in U (N ) Chern-Simons theory. The formula was proposed by Aganagic, Neitzke and Vafa, based on computations involving the conifold transition. We present a more rigorous proof that relies on the universal character for rational representations and an expression of the modular S-matrix in terms of the specialization of characters.

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“…Besides the trivial links, a general formula seems to exist in the mathematics literature only for the Hopf link [14]. In the physics literature, Witten's Chern-Simons path integral with the gauge group SU N [21] offers an intrinsic but not rigorous definition of the colored HOMFLY polynomial.…”

Section: Introductionmentioning

confidence: 99%

On the Hecke algebras and the colored HOMFLY polynomial

Lin

Zheng²

2009

Trans. Amer. Math. Soc.

100

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Abstract. The colored HOMFLY polynomial is the quantum invariant of oriented links in S 3 associated with irreducible representations of the quantum group U q (sl N ). In this paper, using an approach to calculate quantum invariants of links via the cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The technique leads to a fairly simple formula for the colored HOMFLY polynomial of torus links. This formula allows us to test the Labastida-Mariño-Vafa conjecture, which reveals a deep relationship between Chern-Simons gauge theory and string theory, on torus links.

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The Homfly Polynomial of the Decorated Hopf Link

Cited by 62 publications

References 9 publications

The Topological Vertex

The Topological Vertex

Universal character and large N factorization in topological gauge/string theory

On the Hecke algebras and the colored HOMFLY polynomial

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