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Super-A-polynomials for twist knots

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Abstract

We conjecture formulae of the colored superpolynomials for a class of twist knots K p where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomials for the twist knots with small values of p. The results support the categorified versions of the generalized volume conjecture and the quantum volume conjecture. Furthermore, we obtain the evidence that the Q-deformed A-polynomials can be identified with the augmentation polynomials of knot contact homology in the case of the twist knots.

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Authors and Affiliations

  1. Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada

    Satoshi Nawata

  2. Department of Physics, Indian Institute of Technology Bombay, Mumbai, India, 400076

    P. Ramadevi &  Zodinmawia

  3. Department of Mathematics, Xavier University of Louisiana, New Orleans, LA, 70125, U.S.A

    Xinyu Sun

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  1. Satoshi Nawata
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  2. P. Ramadevi
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  3. Zodinmawia
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  4. Xinyu Sun
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Correspondence to Satoshi Nawata.

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ArXiv ePrint: 1209.1409

With a program by Xinyu Sun.

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Nawata, S., Ramadevi, P., Zodinmawia et al. Super-A-polynomials for twist knots. J. High Energ. Phys. 2012, 157 (2012). https://doi.org/10.1007/JHEP11(2012)157

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