Knot invariants from Virasoro related representation and pretzel knots
Abstract
In this study, we remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants.
- Authors:
- Publication Date:
- Research Org.:
- Rutgers Univ., Piscataway, NJ (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1209581
- Alternate Identifier(s):
- OSTI ID: 1240267
- Grant/Contract Number:
- SC0010008; ARRA-SC0003883; SC0007897; SC0003883
- Resource Type:
- Published Article
- Journal Name:
- Nuclear Physics. B
- Additional Journal Information:
- Journal Name: Nuclear Physics. B Journal Volume: 899 Journal Issue: C; Journal ID: ISSN 0550-3213
- Publisher:
- Elsevier
- Country of Publication:
- Netherlands
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Galakhov, D., Melnikov, D., Mironov, A., and Morozov, A. Knot invariants from Virasoro related representation and pretzel knots. Netherlands: N. p., 2015.
Web. doi:10.1016/j.nuclphysb.2015.07.035.
Galakhov, D., Melnikov, D., Mironov, A., & Morozov, A. Knot invariants from Virasoro related representation and pretzel knots. Netherlands. https://doi.org/10.1016/j.nuclphysb.2015.07.035
Galakhov, D., Melnikov, D., Mironov, A., and Morozov, A. Thu .
"Knot invariants from Virasoro related representation and pretzel knots". Netherlands. https://doi.org/10.1016/j.nuclphysb.2015.07.035.
@article{osti_1209581,
title = {Knot invariants from Virasoro related representation and pretzel knots},
author = {Galakhov, D. and Melnikov, D. and Mironov, A. and Morozov, A.},
abstractNote = {In this study, we remind the method to calculate colored Jones polynomials for the plat representations of knot diagrams from the knowledge of modular transformation (monodromies) of Virasoro conformal blocks with insertions of degenerate fields. As an illustration we use a rich family of pretzel knots, lying on a surface of arbitrary genus g, which was recently analyzed by the evolution method. Further generalizations can be to generic Virasoro modular transformations, provided by integral kernels, which can lead to the Hikami invariants.},
doi = {10.1016/j.nuclphysb.2015.07.035},
journal = {Nuclear Physics. B},
number = C,
volume = 899,
place = {Netherlands},
year = {Thu Oct 01 00:00:00 EDT 2015},
month = {Thu Oct 01 00:00:00 EDT 2015}
}
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