Chern-Simons perturbative series revisited

A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with SU(N) gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra ZU(slN) is introduced. This basis allows one to present group factors...

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Autores principales:	E. Lanina, A. Sleptsov, N. Tselousov
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/9947d24d95cf40c7b084d983905cb831
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spelling	oai:doaj.org-article:9947d24d95cf40c7b084d983905cb8312021-12-04T04:32:27ZChern-Simons perturbative series revisited0370-269310.1016/j.physletb.2021.136727https://doaj.org/article/9947d24d95cf40c7b084d983905cb8312021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S0370269321006675https://doaj.org/toc/0370-2693A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with SU(N) gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra ZU(slN) is introduced. This basis allows one to present group factors in an arbitrary irreducible finite-dimensional representation. Developed methods have wide applications, the most straightforward and evident ones are mentioned. Namely, Vassiliev invariants of higher orders are computed, a conjecture about existence of new symmetries of the colored HOMFLY polynomials is stated, and the recently discovered tug-the-hook symmetry of the colored HOMFLY polynomial is proved.E. LaninaA. SleptsovN. TselousovElsevierarticlePhysicsQC1-999ENPhysics Letters B, Vol 823, Iss , Pp 136727- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 E. Lanina A. Sleptsov N. Tselousov Chern-Simons perturbative series revisited
description	A group-theoretical structure in a perturbative expansion of the Wilson loops in the 3d Chern-Simons theory with SU(N) gauge group is studied in symmetric approach. A special basis in the center of the universal enveloping algebra ZU(slN) is introduced. This basis allows one to present group factors in an arbitrary irreducible finite-dimensional representation. Developed methods have wide applications, the most straightforward and evident ones are mentioned. Namely, Vassiliev invariants of higher orders are computed, a conjecture about existence of new symmetries of the colored HOMFLY polynomials is stated, and the recently discovered tug-the-hook symmetry of the colored HOMFLY polynomial is proved.
format	article
author	E. Lanina A. Sleptsov N. Tselousov
author_facet	E. Lanina A. Sleptsov N. Tselousov
author_sort	E. Lanina
title	Chern-Simons perturbative series revisited
title_short	Chern-Simons perturbative series revisited
title_full	Chern-Simons perturbative series revisited
title_fullStr	Chern-Simons perturbative series revisited
title_full_unstemmed	Chern-Simons perturbative series revisited
title_sort	chern-simons perturbative series revisited
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/9947d24d95cf40c7b084d983905cb831
work_keys_str_mv	AT elanina chernsimonsperturbativeseriesrevisited AT asleptsov chernsimonsperturbativeseriesrevisited AT ntselousov chernsimonsperturbativeseriesrevisited
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Chern-Simons perturbative series revisited

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