Wilson loop invariants from WN conformal blocks
Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2015-12-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321315003776 |
| _version_ | 1811261597345120256 |
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| author | Oleg Alekseev Fábio Novaes |
| author_facet | Oleg Alekseev Fábio Novaes |
| author_sort | Oleg Alekseev |
| collection | DOAJ |
| description | Knot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N), which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra. |
| first_indexed | 2024-04-12T19:07:22Z |
| format | Article |
| id | doaj.art-020c66d0a81a44e0b4010573a58b44e2 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-04-12T19:07:22Z |
| publishDate | 2015-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-020c66d0a81a44e0b4010573a58b44e22022-12-22T03:19:59ZengElsevierNuclear Physics B0550-32131873-15622015-12-01901C46147910.1016/j.nuclphysb.2015.11.002Wilson loop invariants from WN conformal blocksOleg AlekseevFábio NovaesKnot and link polynomials are topological invariants calculated from the expectation value of loop operators in topological field theories. In 3D Chern–Simons theory, these invariants can be found from crossing and braiding matrices of four-point conformal blocks of the boundary 2D CFT. We calculate crossing and braiding matrices for WN conformal blocks with one component in the fundamental representation and another component in a rectangular representation of SU(N), which can be used to obtain HOMFLY knot and link invariants for these cases. We also discuss how our approach can be generalized to invariants in higher-representations of WN algebra.http://www.sciencedirect.com/science/article/pii/S0550321315003776 |
| spellingShingle | Oleg Alekseev Fábio Novaes Wilson loop invariants from WN conformal blocks Nuclear Physics B |
| title | Wilson loop invariants from WN conformal blocks |
| title_full | Wilson loop invariants from WN conformal blocks |
| title_fullStr | Wilson loop invariants from WN conformal blocks |
| title_full_unstemmed | Wilson loop invariants from WN conformal blocks |
| title_short | Wilson loop invariants from WN conformal blocks |
| title_sort | wilson loop invariants from wn conformal blocks |
| url | http://www.sciencedirect.com/science/article/pii/S0550321315003776 |
| work_keys_str_mv | AT olegalekseev wilsonloopinvariantsfromwnconformalblocks AT fabionovaes wilsonloopinvariantsfromwnconformalblocks |