Torus Knot Polynomials and Susy Wilson Loops
We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987 ), a basic hypergeometric representation of the HOMFLY polynomial of ( n , m ) torus knots, and present a number of equivalent expressions, all related by Heine’s transformations. Using this result, the ( m , n ) ↔ (...
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| Vydáno v: | Letters in mathematical physics Ročník 104; číslo 12; s. 1535 - 1556 |
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| Jazyk: | angličtina |
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01.12.2014
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| ISSN: | 0377-9017, 1573-0530 |
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| Abstract | We give, using an explicit expression obtained in (Jones V, Ann Math 126:335,
1987
), a basic hypergeometric representation of the HOMFLY polynomial of (
n
,
m
) torus knots, and present a number of equivalent expressions, all related by Heine’s transformations. Using this result, the
(
m
,
n
)
↔
(
n
,
m
)
symmetry and the leading polynomial at large
N
are explicit. We show the latter to be the Wilson loop of 2d Yang–Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang–Mills theory, which is known to give averages of Wilson loops in
N
= 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones–Rosso representation in terms of
q
-harmonic oscillators. |
|---|---|
| AbstractList | We give, using an explicit expression obtained in (Jones V, Ann Math 126:335,
1987
), a basic hypergeometric representation of the HOMFLY polynomial of (
n
,
m
) torus knots, and present a number of equivalent expressions, all related by Heine’s transformations. Using this result, the
(
m
,
n
)
↔
(
n
,
m
)
symmetry and the leading polynomial at large
N
are explicit. We show the latter to be the Wilson loop of 2d Yang–Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang–Mills theory, which is known to give averages of Wilson loops in
N
= 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones–Rosso representation in terms of
q
-harmonic oscillators. |
| Author | Giasemidis, Georgios Tierz, Miguel |
| Author_xml | – sequence: 1 givenname: Georgios surname: Giasemidis fullname: Giasemidis, Georgios organization: Rudolf Peierls Centre for Theoretical Physics, University of Oxford – sequence: 2 givenname: Miguel surname: Tierz fullname: Tierz, Miguel email: tierz@mat.ucm.es organization: Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid |
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| CitedBy_id | crossref_primary_10_1088_1742_5468_2016_01_013103 crossref_primary_10_1007_JHEP08_2019_165 crossref_primary_10_1016_j_nuclphysb_2021_115582 crossref_primary_10_1088_1751_8121_ad421b crossref_primary_10_1364_OL_546177 |
| Cites_doi | 10.1080/10586458.2006.10128956 10.1142/9789812798329_0012 10.1016/0040-9383(87)90025-5 10.1090/S0002-9939-1987-0894448-2 10.1142/S0218216593000064 10.1016/0003-4916(81)90075-0 10.1016/0550-3213(80)90072-3 10.1016/S1385-7258(89)80020-4 10.1088/0305-4470/22/21/020 10.1007/BF01243905 10.1016/0040-9383(90)90021-B 10.1007/BF01217730 10.1090/S0273-0979-1985-15361-3 10.1063/1.3377965 10.1016/0370-2693(94)91447-8 10.2307/1971403 10.1007/BF02102094 10.1142/S0217732390000780 10.1007/BF01445208 10.1016/0001-8708(76)90186-9 10.1016/0550-3213(81)90239-X 10.1103/PhysRevD.77.047901 10.1007/978-3-642-05014-5 10.1007/s00023-010-0058-z 10.1016/0550-3213(93)90402-B 10.1103/PhysRevD.86.045027 10.1088/1126-6708/2005/03/047 10.1016/S0550-3213(00)00300-X 10.1063/1.4758795 10.1088/1126-6708/2008/05/017 10.1088/1126-6708/2008/05/077 10.1142/S0217732304014100 10.1007/978-94-010-9787-1_4 10.1088/1126-6708/2008/06/083 10.1007/JHEP06(2012)048 10.1016/S0550-3213(99)00474-5 10.1007/JHEP07(2010)088 10.1007/s00023-012-0171-2 10.1103/PhysRevD.76.107703 |
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| Keywords | 15B52 HOMFLY polynomial Random matrix models Basic hypergeometric functions 57M27 33D15 |
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| Snippet | We give, using an explicit expression obtained in (Jones V, Ann Math 126:335,
1987
), a basic hypergeometric representation of the HOMFLY polynomial of (
n
,
m... |
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| SubjectTerms | Complex Systems Geometry Group Theory and Generalizations Mathematical and Computational Physics Physics Physics and Astronomy Theoretical |
| Title | Torus Knot Polynomials and Susy Wilson Loops |
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