Knot invariants from Virasoro related representation and pretzel knots
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...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2015-10-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321315002758 |
| _version_ | 1811344238897528832 |
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| author | D. Galakhov D. Melnikov A. Mironov A. Morozov |
| author_facet | D. Galakhov D. Melnikov A. Mironov A. Morozov |
| author_sort | D. Galakhov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-13T19:44:15Z |
| format | Article |
| id | doaj.art-4b279baec0214cb0806c5ff7c5ad662d |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-04-13T19:44:15Z |
| publishDate | 2015-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-4b279baec0214cb0806c5ff7c5ad662d2022-12-22T02:32:47ZengElsevierNuclear Physics B0550-32131873-15622015-10-01899C19422810.1016/j.nuclphysb.2015.07.035Knot invariants from Virasoro related representation and pretzel knotsD. Galakhov0D. Melnikov1A. Mironov2A. Morozov3ITEP, Moscow 117218, RussiaITEP, Moscow 117218, RussiaLebedev Physics Institute, Moscow 119991, RussiaITEP, Moscow 117218, RussiaWe 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.http://www.sciencedirect.com/science/article/pii/S0550321315002758 |
| spellingShingle | D. Galakhov D. Melnikov A. Mironov A. Morozov Knot invariants from Virasoro related representation and pretzel knots Nuclear Physics B |
| title | Knot invariants from Virasoro related representation and pretzel knots |
| title_full | Knot invariants from Virasoro related representation and pretzel knots |
| title_fullStr | Knot invariants from Virasoro related representation and pretzel knots |
| title_full_unstemmed | Knot invariants from Virasoro related representation and pretzel knots |
| title_short | Knot invariants from Virasoro related representation and pretzel knots |
| title_sort | knot invariants from virasoro related representation and pretzel knots |
| url | http://www.sciencedirect.com/science/article/pii/S0550321315002758 |
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