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Colored HOMFLY polynomials of knots presented as double fat diagrams

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Title Colored HOMFLY polynomials of knots presented as double fat diagrams
 
Creator MIRONOV, A
MOROZOV, A
MOROZOV, A
RAMADEVI, P
SINGH, VK
 
Subject CHERN-SIMONS THEORY
GENUS EXPANSION
DIFFERENTIAL HIERARCHY
DISTINGUISHING MUTANTS
MATRIX FACTORIZATIONS
QUANTUM GROUPS
LINK HOMOLOGY
INVARIANTS
ALGEBRA
REPRESENTATIONS
Quantum Groups
Chern-Simons Theories
Topological Field Theories
 
Description Many knots and links in S-3 can be drawn as gluing of three manifolds with one or more four-punctured S-2 boundaries. We call these knot diagrams as double fat graphs whose invariants involve only the knowledge of the fusion and the braiding matrices of four-strand braids. Incorporating the properties of four-point conformal blocks in WZNW models, we conjecture colored HOMFLY polynomials for these double fat graphs where the color can be rectangular or non-rectangular representation. With the recent work of Gu-Jockers, the fusion matrices for the non-rectangular [21] representation, the first which involves multiplicity is known. We verify our conjecture by comparing with the [21] colored HOMFLY of many knots, obtained as closure of three braids. The conjectured form is computationally very effective leading to writing [21]-colored HOMFLY polynomials for many pretzel type knots and non-pretzel type knots. In particular, we find class of pretzel mutants which are distinguished and another class of mutants which cannot be distinguished by [21] representation. The difference between the [21]-colored HOMFLY of two mutants seems to have a general form, with A-dependence completely defined by the old conjecture due to Morton and Cromwell. In particular, we check it for an entire multi-parametric family of mutant knots evaluated using evolution method.
 
Publisher SPRINGER
 
Date 2016-01-14T10:50:23Z
2016-01-14T10:50:23Z
2015
 
Type Article
 
Identifier JOURNAL OF HIGH ENERGY PHYSICS(7)
1029-8479
http://dx.doi.org/10.1007/JHEP07(2015)109
http://dspace.library.iitb.ac.in/jspui/handle/100/17402
 
Language en