Universität zu Köln

Banerjee, Sibasish, Jankowski, Jakub and Sulkowski, Piotr (2020). Revisiting the Melvin-Morton-Rozansky expansion, or there and back again. J. High Energy Phys. (12). NEW YORK: SPRINGER. ISSN 1029-8479

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Abstract

Alexander polynomial arises in the leading term of a semi-classical Melvin-Morton-Rozansky expansion of colored knot polynomials. In this work, following the opposite direction, we propose how to reconstruct colored HOMFLY-PT polynomials, superpolynomials, and newly introduced Z<mml:mo stretchy=true></mml:mover> invariants for some knot complements, from an appropriate rewriting, quantization and deformation of Alexander polynomial. Along this route we rederive conjectural expressions for the above mentioned invariants for various knots obtained recently, thereby proving their consistency with the Melvin-Morton-Rozansky theorem, and derive new formulae for colored superpolynomials unknown before. For a given knot, depending on certain choices, our reconstruction leads to equivalent expressions, which are either cyclotomic, or encode certain features of HOMFLY-PT homology and the knots-quivers correspondence.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Banerjee, Sibasish UNSPECIFIED UNSPECIFIED UNSPECIFIED Jankowski, Jakub UNSPECIFIED UNSPECIFIED UNSPECIFIED Sulkowski, Piotr UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-307974
DOI:	10.1007/JHEP12(2020)095
Journal or Publication Title:	J. High Energy Phys.
Number:	12
Date:	2020
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1029-8479
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language KNOTS; INVARIANT; ALGEBRA Multiple languages Physics, Particles & Fields Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/30797