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Difference of Mutant Knot Invariants and Their Differential Expansion

  • Methods of Theoretical Physics
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Abstract

We evaluate the differences of HOMFLY-PT invariants for pairs of mutant knots colored with representations of SL(N), which are large enough to distinguish between them. These mutant pairs include the pretzel mutants, which require at least the representation, labelled by the Young diagram [2, 4]. We discuss the differential expansion for the differences, which is nontrivial in the case of mutants with a nonzero defect. The most effective technical tool in this case turns out to be the standard Reshetikhin-Turaev approach.

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Funding

This work was supported in part by the Foundation for the Advancement of Theoretical Physics “BASIS” (L. Bishler, A. Mironov, A. Morozov, An. Morozov, A. Sleptsov), by the Council of the President of the Russian Federation for State Support of Young Scientists and Leading Scientific Schools (project no. MK-2038.2019, L. Bishler, An. Morozov), by the Russian Foundation for Basic Research (project no. 19-01-00680, A. Mironov; project no. 19-02-00815, A. Morozov; project no. 20-01-00644, An. Morozov, A. Sleptsov; project no. 18-31-20046-mol-a-ved, A. Sleptsov), by joint grant nos. 19-51-50008-YaF-a (L. Bishler, A. Mironov, An. Morozov), 19-51-53014-GFEN-a, 18-51-05015-Arm-a, 18-51-45010-IND-a (L. Bishler, A. Mironov, A. Morozov, An. Morozov, A. Sleptsov). P. Ramadevi, Vivek Kumar Singh, and Saswati Dhara acknowledge the support of the Department of Science and Technology (DST), Government of India and the Russian Foundation for Basic Research (grant no. INT/RUS/RFBR/P-231). The work was also partly supported jointly by the Russian Foundation for Basic Research and NSFB (project no. 1951-18006 (A. Mironov, A. Morozov, An. Morozov). Vivek Kumar Singh is grateful to the Indian Institute of Science Education and Research (Pune, India) for hospitality. A. Mironov, A. Morozov, and P. Ramadevi also acknowledge the hospitality of KITP and partial support of the National Science Foundation (grant no. NSF PHY1748958).

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Authors and Affiliations

  1. Lebedev Physics Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    L. Bishler & A. Mironov

  2. Institute for Theoretical and Experimental Physics, National Research Center Kurchatov Institute, Moscow, 117218, Russia

    L. Bishler, A. Mironov, A. Morozov, An. Morozov & A. Sleptsov

  3. Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, 127994, Russia

    L. Bishler, A. Mironov, A. Morozov, An. Morozov & A. Sleptsov

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

    Saswati Dhara, P. Ramadevi & Vivek Kumar Singh

  5. Moscow Institute of Physics and Technology, National Research University, Dolgoprudnyi, Moscow region, 141701, Russia

    T. Grigoryev, A. Morozov, An. Morozov & A. Sleptsov

Authors
  1. L. Bishler
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  2. Saswati Dhara
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  3. T. Grigoryev
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  4. A. Mironov
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  5. A. Morozov
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  6. An. Morozov
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  7. P. Ramadevi
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  8. Vivek Kumar Singh
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  9. A. Sleptsov
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Corresponding authors

Correspondence to L. Bishler, Saswati Dhara, T. Grigoryev, A. Mironov, A. Morozov, An. Morozov, P. Ramadevi, Vivek Kumar Singh or A. Sleptsov.

Additional information

Published in Russian in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2020, Vol. 111, No. 9, pp. 591–596.

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Bishler, L., Dhara, S., Grigoryev, T. et al. Difference of Mutant Knot Invariants and Their Differential Expansion. Jetp Lett. 111, 494–499 (2020). https://doi.org/10.1134/S0021364020090015

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  • DOI: https://doi.org/10.1134/S0021364020090015

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