Distinguishing Mutant knots

Bishler, L.; Dhara, Saswati; Grigoryev, T.; Mironov, A.; Morozov, A.; Morozov, An.; Ramadevi, P.; Singh, Vivek Kumar; Sleptsov, A.

doi:10.1016/j.geomphys.2020.103928

Distinguishing Mutant knots

L. Bishler
(
- Lebedev Inst. and
- Moscow, ITEP and
- IITP, Moscow
)
,
Saswati Dhara
(
- Indian Inst. Tech., Mumbai
)
,
T. Grigoryev
(
- Moscow, MIPT
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP and
- IITP, Moscow
)
,
A. Morozov
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)

Jul 24, 2020

30 pages

Published in:

J.Geom.Phys. 159 (2021) 103928

Published: Sep 12, 2020
and
Published: Jan, 2021

e-Print:

2007.12532 [hep-th]

DOI:

10.1016/j.geomphys.2020.103928 (publication)

Report number:

FIAN/TD-12/20; IITP/TH-09/20; ITEP/TH-12/20; MIPT/TH-09/20

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Abstract: (Elsevier B.V.)

Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical and mathematical theories. One of the challenging problems in knot theory is distinguishing mutant knots. Mutant knots are not distinguished by colored HOMFLY-PT polynomials for knots colored by either symmetric and or antisymmetric representations of

S U (N)

. Some of the mutant knots can be distinguished by the simplest non-symmetric representation

[2, 1]

. However there is a class of mutant knots which require more complex representations like

[4, 2]

. In this paper we calculate polynomials and differences for the mutant knot polynomials in representations

[3, 1]

and

[4, 2]

and study their properties.

Note:

22 pages + 3 Appendices

Chern–Simons theory
Knot theory
Mutant knots
HOMFLY-PT polynomials
knot theory
Chern-Simons term
representation: SU(N)
R-matrix
quantum group
braid group

References(119)

Figures(5)

[1]

Y. Akutsu
,
T. Deguchi
,
T. Ohtsuki

- J.Knot Theor.Ramifications 1 (1992) 161

[2]

Knots, Links, Braids and Exactly Solvable Models in Statistical Mechanics

Yasuhiro Akutsu
(
- Kanagawa U.
)
,
Miki Wadati
(
- Tokyo U., Komaba
)

- Commun.Math.Phys. 117 (1988) 243
•
DOI:
- 10.1007/BF01223592

[3]

Interplay between symmetries of quantum 6j-symbols and the eigenvalue hypothesis

Victor Alekseev
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)
,
Andrey Morozov
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)
,
Alexey Sleptsov
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)

- Lett.Math.Phys. 111 (2021) 2, 50,
- Lett.Math.Phys. 111 (2021) 50
•
e-Print:
- 1909.07601
•
DOI:
- 10.1007/s11005-021-01386-1

[4]

Multiplicity-free $U_q (sl_N)$ 6-j symbols: Relations, asymptotics, symmetries

Victor Alekseev
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)
,
Andrey Morozov
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)
,
Alexey Sleptsov
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)

- Nucl.Phys.B 960 (2020) 115164
•
e-Print:
- 1912.13325
•
DOI:
- 10.1016/j.nuclphysb.2020.115164

[5]

N. Amburg
,
A. Orlov
,
D. Vasiliev

- Entropy 22.9:972 (2020)

[6]

On R-matrix approaches to knot invariants

A. Anokhina
(
- Moscow, ITEP
)

e-Print:
- 1412.8444

[7]

Colored HOMFLY polynomials as multiple sums over paths or standard Young tableaux

A. Anokhina
(
- Moscow, MIPT and
- Moscow, ITEP
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)
,
And. Morozov
(
- Moscow State U. and
- Moscow, ITEP
)

- Adv.High Energy Phys. 2013 (2013) 931830
•
e-Print:
- 1304.1486
•
DOI:
- 10.1155/2013/931830

[8]

Racah coefficients and extended HOMFLY polynomials for all 5-, 6- and 7-strand braids

A. Anokhina
(
- Moscow, MIPT and
- Moscow, ITEP
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)
,
And. Morozov
(
- Moscow State U. and
- Moscow, ITEP
)

- Nucl.Phys.B 868 (2013) 271-313
•
e-Print:
- 1207.0279
•
DOI:
- 10.1016/j.nuclphysb.2012.11.006

[9]

Knot polynomials in the first non-symmetric representation

A. Anokhina
(
- Moscow, MIPT and
- Moscow, ITEP
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP and
- IIP, Brazil
)
,
A. Morozov
(
- Moscow, ITEP and
- IIP, Brazil
)
,
An. Morozov
(
- Moscow State U. and
- Moscow, ITEP
)

- Nucl.Phys.B 882 (2014) 171-194
•
e-Print:
- 1211.6375
•
DOI:
- 10.1016/j.nuclphysb.2014.03.002

[10]

Cabling procedure for the colored HOMFLY polynomials

A. Anokhina
(
- Moscow, MIPT and
- Moscow, ITEP
)
,
An. Morozov
(
- Moscow State U. and
- Moscow, ITEP
)

- Teor.Mat.Fiz. 178 (2014) 3-68,
- Theor.Math.Phys. 178 (2014) 1, 1-58
•
e-Print:
- 1307.2216
•
DOI:
- 10.1007/s11232-014-0129-2

[11]

Nimble evolution for pretzel Khovanov polynomials

Aleksandra Anokhina
(
- Moscow, ITEP
)
,
Alexei Morozov
(
- Moscow, MIPT and
- Moscow, ITEP and
- IITP, Moscow
)
,
Aleksandr Popolitov
(
- Moscow, MIPT and
- Moscow, ITEP and
- Uppsala U. and
- IITP, Moscow
)

- Eur.Phys.J.C 79 (2019) 10, 867
•
e-Print:
- 1904.10277
•
DOI:
- 10.1140/epjc/s10052-019-7303-5

[12]

Differential hierarchy and additional grading of knot polynomials

S.B. Arthamonov
(
- Moscow, ITEP
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP
)
,
A. Morozov
(
- Moscow, ITEP
)

- Theor.Math.Phys. 179 (2014) 509-542,
- Teor.Mat.Fiz. 179 (2014) 147-188
•
e-Print:
- 1306.5682
•
DOI:
- 10.1007/s11232-014-0159-9

[13]

Differential expansion for link polynomials

C. Bai
(
- Nankai, CIM and
- Nankai, LPMC
)
,
J. Jiang
,
J. Liang
(
- Nankai, CIM and
- Nankai, LPMC
)
,
A. Mironov
(
- Moscow, ITEP and
- Lebedev Inst. and
- Moscow Phys. Eng. Inst. and
- IITP, Moscow
)
,
A. Morozov
(
- IITP, Moscow and
- Moscow Phys. Eng. Inst. and
- Moscow, ITEP
)

et al.

- Phys.Lett.B 778 (2018) 197-206
•
e-Print:
- 1709.09228
•
DOI:
- 10.1016/j.physletb.2018.01.026

[14]

Quantum Racah matrices up to level 3 and multicolored link invariants

C. Bai
(
- Nankai, CIM and
- Nankai, LPMC
)
,
J. Jiang
,
J. Liang
(
- Nankai, CIM and
- Nankai, LPMC
)
,
A. Mironov
(
- Lebedev Inst. and
- Moscow, ITEP and
- IITP, Moscow
)
,
A. Morozov
(
- Moscow, ITEP and
- IITP, Moscow
)

et al.

- J.Geom.Phys. 132 (2018) 155-180
•
e-Print:
- 1801.09363
•
DOI:
- 10.1016/j.geomphys.2018.05.020

[15]

Entanglement Entropy and the Colored Jones Polynomial

Vijay Balasubramanian
(
)
,
Matthew DeCross
(
- Pennsylvania U.
)
,
Jackson Fliss
(
- Illinois U., Urbana
)
,
Arjun Kar
(
- Pennsylvania U.
)
,
Robert G. Leigh
(
- Illinois U., Urbana
)

et al.

- JHEP 05 (2018) 038
•
e-Print:
- 1801.01131
•
DOI:
- 10.1007/JHEP05(2018)038

[16]

Multi-Boundary Entanglement in Chern-Simons Theory and Link Invariants

Vijay Balasubramanian
(
- Pennsylvania U.
)
,
Jackson R. Fliss
(
- Illinois U., Urbana
)
,
Robert G. Leigh
(
- Illinois U., Urbana
)
,
Onkar Parrikar
(
- Pennsylvania U.
)

- JHEP 04 (2017) 061
•
e-Print:
- 1611.05460
•
DOI:
- 10.1007/JHEP04(2017)061

[17]

D. Bar-Natan, S. Morrison

- http://katlas.org

[18]

Difference of Mutant Knot Invariants and Their Differential Expansion

L. Bishler
(
- LPI, Moscow (main) and
- Moscow, ITEP and
- IITP, Moscow
)
,
Saswati Dhara
(
- Indian Inst. Tech., Mumbai
)
,
T. Grigoryev
(
- Moscow, MIPT
)
,
A. Mironov
(
- LPI, Moscow (main) and
- Moscow, ITEP and
- IITP, Moscow
)
,
A. Morozov
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)

et al.

- JETP Lett. 111 (2020) 9, 494-499,
- Pisma Zh.Eksp.Teor.Fiz. 111 (2020) 9, 591-596
•
e-Print:
- 2004.06598
•
DOI:
- 10.1134/S0021364020090015

[19]

Perspectives of differential expansion

L. Bishler
(
- Lebedev Inst. and
- Moscow, ITEP and
- IITP, Moscow
)
,
A. Morozov
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)

- Phys.Lett.B 808 (2020) 135639
•
e-Print:
- 2006.01190
•
DOI:
- 10.1016/j.physletb.2020.135639

[20]

On the block structure of the quantum $\mathcal{R}$ -matrix in the three-strand braids

L. Bishler
(
- Moscow State U. and
- Moscow, ITEP
)
,
An. Morozov
(
- Moscow, ITEP and
- IITP, Moscow and
- Moscow, MIPT
)
,
A. Sleptsov
(
- Moscow, ITEP and
- IITP, Moscow and
- Chelyabinsk State U.
)
,
Sh. Shakirov
(
- Harvard U. and
- IITP, Moscow
)

- Int.J.Mod.Phys.A 33 (2018) 17, 1850105,
- International Journal of Modern Physics AVol. 33, No. 17, 1850105 (2018)
•
e-Print:
- 1712.07034
•
DOI:
- 10.1142/S0217751X18501051

[21]

F. Bonahon
,
L.C. Siebenmann

[22]

Torus knots and mirror symmetry

Andrea Brini
(
- Geneva U.
)
,
Bertrand Eynard
(
- CERN and
- Saclay, SPhT
)
,
Marcos Marino
(
- Geneva U.
)

- Annales Henri Poincare 13 (2012) 1873-1910
•
e-Print:
- 1105.2012
•
DOI:
- 10.1007/s00023-012-0171-2

[23]

A. Caudron

[24]

Characteristic forms and geometric invariants

Shiin-Shen Chern
(
- UC, Berkeley
)
,
James Simons
(
- SUNY, Stony Brook
)

- Annals Math. 99 (1974) 48-69
•
DOI:
- 10.2307/1971013

[25]

LeechJohn

J.H. Conway

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3
4
5
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