Tabulating knot polynomials for arborescent knots

Autor: A. D. Mironov, Alexey Sleptsov, Vivek Kumar Singh, P. Ramadevi, A. Morozov
Rok vydání: 2016
Předmět:
Statistics and Probability
High Energy Physics - Theory
Pure mathematics
Computation
Invariants
General Physics and Astronomy
FOS: Physical sciences
Algebras
01 natural sciences
Modular transformation
Matrix model
symbols.namesake
Mathematics - Geometric Topology
Symmetry
Knot (unit)
Knot Theory
0103 physical sciences
Mathematics - Quantum Algebra
FOS: Mathematics
Feynman diagram
Field-Theory
Quantum Algebra (math.QA)
Gauge theory
Representation Theory (math.RT)
010306 general physics
Mathematical Physics
Mathematics
Matrix Models
010308 nuclear & particles physics
Statistical and Nonlinear Physics
Geometric Topology (math.GT)
Arborescent
Mathematics::Geometric Topology
Knot theory
Representation
Topological Field Theory
Chern-Simons Theory
High Energy Physics - Theory (hep-th)
Modeling and Simulation
symbols
Mathematics - Representation Theory
Links
Homfly Polynomials
DOI: 10.48550/arxiv.1601.04199
Popis: Arborescent knots are the ones which can be represented in terms of double fat graphs or equivalently as tree Feynman diagrams. This is the class of knots for which the present knowledge is enough for lifting topological description to the level of effective analytical formulas. The paper describes the origin and structure of the new tables of colored knot polynomials, which will be posted at the dedicated site. Even if formal expressions are known in terms of modular transformation matrices, the computation in finite time requires additional ideas. We use the "family" approach, and apply it to arborescent knots in the Rolfsen table by developing a Feynman diagram technique associated with an auxiliary matrix model field theory. Gauge invariance in this theory helps to provide meaning to Racah matrices in the case of non-trivial multiplicities and explains the need for peculiar sign prescriptions in the calculation of [21]-colored HOMFLY polynomials.
Comment: 19 pages
Databáze: OpenAIRE
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