Chern-Simons matrix models and Stieltjes-Wigert polynomials - INSPIRE

DataBETA

Chern-Simons matrix models and Stieltjes-Wigert polynomials

Sep, 2006

25 pages

Published in:

J.Math.Phys. 48 (2007) 023507

e-Print:

hep-th/0609167 [hep-th]

DOI:

10.1063/1.2436734

Report number:

LPTENS-06-44

View in:

reference search52 citations

Citations per year

Abstract:

Employing the random matrix formulation of Chern-Simons theory on Seifert manifolds, we show how the Stieltjes-Wigert orthogonal polynomials are useful in exact computations in Chern-Simons matrix models. We construct a biorthogonal extension of the Stieltjes-Wigert polynomials, not available in the literature, necessary to study Chern-Simons matrix models when the geometry is a lens space. We also discuss several other results based on the properties of the polynomials: the equivalence between the Stieltjes-Wigert matrix model and the discrete model that appears in q-2D Yang-Mills and the relationship with Rogers-Szego polynomials and the corresponding equivalence with an unitary matrix model. Finally, we also give a detailed proof of a result that relates quantum dimensions with averages of Schur polynomials in the Stieltjes-Wigert ensemble.

02.10.De
02.10.Yn
05.40.-a
11.15.-q
11.25.Yb
02.40.-k
polynomials
Chern-Simons theory
geometry
random processes

References(38)

Figures(0)

Quantum Field Theory and the Jones Polynomial

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Commun.Math.Phys. 121 (1989) 351-399,
•
DOI:
- 10.1007/BF01217730

Les Houches lectures on matrix models and topological strings

Marcos Marino
(
- CERN and
- Lisbon, IST
)

e-Print:
- hep-th/0410165

Chern-Simons theory and topological strings

Marcos Marino
(
- CERN
)

- Rev.Mod.Phys. 77 (2005) 675-720
•
e-Print:
- hep-th/0406005
•
DOI:
- 10.1103/RevModPhys.77.675

Chern-Simons theory, matrix integrals, and perturbative three manifold invariants

Marcos Marino
(
- Harvard U., Phys. Dept.
)

- Commun.Math.Phys. 253 (2004) 25-49
•
e-Print:
- hep-th/0207096
•
DOI:
- 10.1007/s00220-004-1194-4

Chern-Simons gauge theory as a string theory

Edward Witten
(
- Princeton, Inst. Advanced Study
)

- Prog.Math. 133 (1995) 637-678
•
e-Print:
- hep-th/9207094

Topological closed string interpretation of Chern-Simons theory

Vipul Periwal
(
- Princeton, Inst. Advanced Study
)

- Phys.Rev.Lett. 71 (1993) 1295-1298
•
e-Print:
- hep-th/9305115
•
DOI:
- 10.1103/PhysRevLett.71.1295

Chern-Simons-Witten theory as a topological Fermi liquid

Michael R. Douglas
(
- Rutgers U., Piscataway
)

e-Print:
- hep-th/9403119

On the gauge theory / geometry correspondence

Rajesh Gopakumar
(
- Harvard U.
)
,
Cumrun Vafa
(
- Harvard U.
)

- Adv.Theor.Math.Phys. 3 (1999) 1415-1443,
- AMS/IP Stud.Adv.Math. 23 (2001) 45-63
•
e-Print:
- hep-th/9811131
•
DOI:
- 10.4310/ATMP.1999.v3.n5.a5

Knot invariants and topological strings

Hirosi Ooguri
(
- Caltech
)
,
Cumrun Vafa
(
- Harvard U.
)

- Nucl.Phys.B 577 (2000) 419-438
•
e-Print:
- hep-th/9912123
•
DOI:
- 10.1016/S0550-3213(00)00118-8

Soft matrix models and Chern-Simons partition functions

Miguel Tierz
(
- CSIC, Catalunya
)

- Mod.Phys.Lett.A 19 (2004) 1365-1378
•
e-Print:
- hep-th/0212128
•
DOI:
- 10.1142/S0217732304014100

Discrete and oscillatory matrix models in Chern-Simons theory

Sebastian de Haro
(
- Potsdam, Max Planck Inst.
)
,
Miguel Tierz
(
- Barcelona, IEEC and
- Open U., England
)

- Nucl.Phys.B 731 (2005) 225-241
•
e-Print:
- hep-th/0501123
•
DOI:
- 10.1016/j.nuclphysb.2005.09.034

Matrix model as a mirror of Chern-Simons theory

Mina Aganagic
(
- Harvard U.
)
,
Albrecht Klemm
(
- Humboldt U., Berlin
)
,
Marcos Marino
(
- Harvard U.
)
,
Cumrun Vafa
(
- Harvard U.
)

- JHEP 02 (2004) 010
•
e-Print:
- hep-th/0211098
•
DOI:
- 10.1088/1126-6708/2004/02/010

Chern-Simons matrix models and unoriented strings

- JHEP 02 (2004) 002
•
e-Print:
- hep-th/0305134
•
DOI:
- 10.1088/1126-6708/2004/02/002

Large N duality, lens spaces and the Chern-Simons matrix model

Nick Halmagyi
(
- Southern California U. and
- Santa Barbara, KITP
)
,
Takuya Okuda
(
- Caltech
)
,
Vadim Yasnov
(
- Southern California U.
)

- JHEP 04 (2004) 014
•
e-Print:
- hep-th/0312145
•
DOI:
- 10.1088/1126-6708/2004/04/014

The Spectral curve of the lens space matrix model

Nick Halmagyi
(
- Southern California U. and
- Santa Barbara, KITP
)
,
Vadim Yasnov
(
- Southern California U.
)

- JHEP 11 (2009) 104
•
e-Print:
- hep-th/0311117
•
DOI:
- 10.1088/1126-6708/2009/11/104

Chern-Simons matrix model for local conifold

Vadim Yasnov
(
- Southern California U.
)

e-Print:
- hep-th/0409136

Derivation of Calabi-Yau crystals from Chern-Simons gauge theory

Takuya Okuda
(
- Caltech
)

- JHEP 03 (2005) 047
•
e-Print:
- hep-th/0409270
•
DOI:
- 10.1088/1126-6708/2005/03/047

From effective actions to the background geometry

A. Gorsky
(
- Moscow, ITEP and
- Minnesota U., Theor. Phys. Inst.
)
,
V. Lysov
(
- Moscow, ITEP and
- Moscow, MIPT
)

- Nucl.Phys.B 718 (2005) 293-318
•
e-Print:
- hep-th/0411063
•
DOI:
- 10.1016/j.nuclphysb.2005.04.020

Brownian motion, Chern-Simons theory, and 2-D Yang-Mills

Sebastian de Haro
(
- Potsdam, Max Planck Inst.
)
,
Miguel Tierz
(
- Open U., England and
- Barcelona, IEEC and
- CSIC, Catalunya
)

- Phys.Lett.B 601 (2004) 201-208
•
e-Print:
- hep-th/0406093
•
DOI:
- 10.1016/j.physletb.2004.09.033

Black holes, q-deformed 2d Yang-Mills, and non-perturbative topological strings

Mina Aganagic
(
- UC, Berkeley
)
,
Hirosi Ooguri
(
- Caltech
)
,
Natalia Saulina
(
- Harvard U., Phys. Dept.
)
,
Cumrun Vafa
(
- Harvard U., Phys. Dept.
)

- Nucl.Phys.B 715 (2005) 304-348
•
e-Print:
- hep-th/0411280
•
DOI:
- 10.1016/j.nuclphysb.2005.02.035

Topological strings and large N phase transitions. I. Nonchiral expansion of q-deformed Yang-Mills theory

Nicola Caporaso
(
- Florence U. and
- INFN, Florence
)
,
Michele Cirafici
(
- Heriot-Watt U.
)
,
Luca Griguolo
(
- Parma U. and
- INFN, Parma
)
,
Sara Pasquetti
(
- Parma U. and
- INFN, Parma
)
,
Domenico Seminara
(
- Florence U. and
- INFN, Florence
)

et al.

- JHEP 01 (2006) 035
•
e-Print:
- hep-th/0509041
•
DOI:
- 10.1088/1126-6708/2006/01/035

Topological strings and large N phase transitions. II. Chiral expansion of q-deformed Yang-Mills theory

Nicola Caporaso
(
- Florence U. and
- INFN, Florence
)
,
Michele Cirafici
(
- Heriot-Watt U.
)
,
Luca Griguolo
(
- Parma U. and
- INFN, Parma
)
,
Sara Pasquetti
(
- Parma U. and
- INFN, Parma
)
,
Domenico Seminara
(
- Florence U. and
- INFN, Florence
)

et al.

- JHEP 01 (2006) 036
•
e-Print:
- hep-th/0511043
•
DOI:
- 10.1088/1126-6708/2006/01/036

Phase transitions in q-deformed 2-D Yang-Mills theory and topological strings

Xerxes Arsiwalla
(
- Amsterdam U.
)
,
Rutger Boels
(
- Amsterdam U.
)
,
Marcos Marino
(
- CERN and
- Lisbon, IST Maths
)
,
Annamaria Sinkovics
(
- Amsterdam U.
)

- Phys.Rev.D 73 (2006) 026005
•
e-Print:
- hep-th/0509002
•
DOI:
- 10.1103/PhysRevD.73.026005

A DK phase transition in q-deformed Yang-Mills on S**2 and topological strings

Daniel Jafferis
(
- Harvard U.
)
,
Joseph Marsano
(
- Harvard U.
)

e-Print:
- hep-th/0509004

Black-holes, topological strings and large N phase transitions

Nicola Caporaso
(
- Florence U. and
- INFN, Florence
)
,
Michele Cirafici
(
- Heriot-Watt U.
)
,
L. Griguolo
(
- Parma U. and
- INFN, Parma
)
,
Sara Pasquetti
(
- Parma U. and
- INFN, Parma
)
,
D. Seminara
(
- Florence U. and
- INFN, Florence
)

et al.

- J.Phys.Conf.Ser. 33 (2006) 13-25
•
e-Print:
- hep-th/0512213
•
DOI:
- 10.1088/1742-6596/33/1/002

1-25 of 38
1
2
25 / page