Wilson loop invariants from WN conformal blocks

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...

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Main Authors: Oleg Alekseev, Fábio Novaes
Format: Article
Language:English
Published: Elsevier 2015-12-01
Series:Nuclear Physics B
Online Access:http://www.sciencedirect.com/science/article/pii/S0550321315003776
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spelling doaj-020c66d0a81a44e0b4010573a58b44e22020-11-24T22:59:20ZengElsevierNuclear 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
collection DOAJ
language English
format Article
sources DOAJ
author Oleg Alekseev
Fábio Novaes
spellingShingle Oleg Alekseev
Fábio Novaes
Wilson loop invariants from WN conformal blocks
Nuclear Physics B
author_facet Oleg Alekseev
Fábio Novaes
author_sort Oleg Alekseev
title Wilson loop invariants from WN conformal blocks
title_short 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_sort wilson loop invariants from wn conformal blocks
publisher Elsevier
series Nuclear Physics B
issn 0550-3213
1873-1562
publishDate 2015-12-01
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.
url http://www.sciencedirect.com/science/article/pii/S0550321315003776
work_keys_str_mv AT olegalekseev wilsonloopinvariantsfromwnconformalblocks
AT fabionovaes wilsonloopinvariantsfromwnconformalblocks
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