Chern-Simons matrix models, two-dimensional Yang-Mills theory and the Sutherland model

Journal of Physics A: Mathematical and Theoretical

Volumn 43, Issue 26, 2010, Pages

  Szabo, Richard J ^a,b   Tierz, Miguel ^c  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b MAXWELL INSTITUTE FOR MATHEMATICAL SCIENCES   (United Kingdom)

^c UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953349108     PISSN: 17518113     EISSN: 17518121     Source Type: Journal    
DOI: 10.1088/1751-8113/43/26/265401     Document Type: Article

References (58)

1. Brézin E, Itzykson C, Parisi G and Zuber J-B 1978 Planar diagrams Commun. Math. Phys. 59 35-51
2. Mehta M L 1991 Random Matrices (Boston, MA: Academic)
3. Witten E 1989 Quantum field theory and the Jones polynomial Commun. Math. Phys. 121 351-99
4. Cordes S, Moore G W and Ramgoolam S 1995 Lectures on 2D Yang-Mills theory, equivariant cohomology and topological field theories Nucl. Phys. Proc. Suppl. 41 184-244 (arXiv:hep-th/9411210)
5. Klimík C 2001 The formulae of Kontsevich and Verlinde from the perspective of the Drinfel'd double Commun. Math. Phys. 217 203-28 (arXiv:hep-th/9911239)
6. Aganagic M, Ooguri H, Saulina N and Vafa C 2005 Black holes, q-deformed 2D Yang-Mills, and non-perturbative topological strings Nucl. Phys. B 715 304-48 (arXiv:hep-th/0411280)
7. Altland A and Zirnbauer M R 1997 Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures Phys. Rev. B 55 1142-61 (arXiv:cond-mat/9602137)
8. Caselle M and Magnea U 2004 Random matrix theory and symmetric spaces Phys. Rep. 394 41-156 (arXiv:cond-mat/0304363)
9. Zirnbauer M R 2006 Symmetry classes in random matrix theory Encyclopedia of Mathematical Physics ed Francoise J P, Naber G L and Tsun T S (Oxford: Academic) (arXiv:math-ph/0404058)
10. Zirnbauer M R 2010 Symmetry classes arXiv:1001.0722 [math-ph]
11. Mariño M 2004 Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants Commun. Math. Phys. 253 25-49 (arXiv:hep-th/0207096)
12. Aganagic M, Klemm A, Mariño M and Vafa C 2004 Matrix model as a mirror of Chern-Simons theory J. High Energy Phys. JHEP02(2004)010 (arXiv:hep-th/0211098)
13. Forrester P J 1989 Vicious random walkers in the limit of a large number of walkers J. Stat. Phys. 56 767-82
14. Tierz M 2004 Soft matrix models and Chern-Simons partition functions Mod. Phys. Lett. A 19 1365-78 (arXiv:hep-th/0212128)
15. Dolivet Y and Tierz M 2007 Chern-Simons matrix models and Stieltjes-Wigert polynomials J. Math. Phys. 48 023507 (arXiv:hep-th/0609167)
16. Okuda T 2005 Derivation of Calabi-Yau crystals from Chern-Simons gauge theory J. High Energy Phys. JHEP03(2005)047 (arXiv:hep-th/0409270)
17. Beasley C and Witten E 2005 Non-Abelian localization for Chern-Simons theory J. Diff. Geom. 70 183-323 (arXiv:hep-th/0503126)
18. 1-bundles: Abelianisation and q-deformed Yang-Mills theory J. High Energy Phys. JHEP05(2006)003 (arXiv:hep-th/0601068)
19. Caporaso N, Cirafici M, Griguolo L, Pasquetti S, Seminara D and Szabo R J 2006 Topological strings and large N phase transitions: I. Nonchiral expansion of q-deformed Yang-Mills theory J. High Energy Phys. JHEP01(2006)035 (arXiv:hep-th/0509041)
20. Caporaso N, Cirafici M, Griguolo L, Pasquetti S, Seminara D and Szabo R J 2006 Black holes, topological strings and large N phase transitions J. Phys. Conf. Ser. 33 13-25 (arXiv:hep-th/0512213)
21. Griguolo L, Seminara D, Szabo R J and Tanzini A 2007 Black holes, instanton counting on toric singularities and q-deformed two-dimensional Yang-Mills theory Nucl. Phys. B 772 1-24 (arXiv:hep-th/0610155)
22. Okuyama K 2007 D-brane amplitudes in topological string on conifold Phys. Lett. B 645 275-80 (arXiv:hep-th/0606048)
23. Douglas M R and Kazakov V A 1993 Large N phase transition in continuum QCD in two dimensions Phys. Lett. B 319 219-30 (arXiv:hep-th/9305047)
24. Gross D J and Matytsin A 1994 Instanton induced large N phase transitions in two-dimensional and four-dimensional QCD Nucl. Phys. B 429 50-74 (arXiv:hep-th/9404004)
25. Periwal V and Shevitz D 1990 Unitary matrix models as exactly solvable string theories Phys. Rev. Lett. 64 1326-9
26. Periwal V and Shevitz D 1990 Exactly solvable unitary matrix models: multicritical potentials and correlations Nucl. Phys. B 344 731-46
27. Dijkgraaf R and Vafa C 2002 On geometry and matrix models Nucl. Phys. B 644 21-39 (arXiv:hep-th/0207106)
28. Klebanov I R, Maldacena J M and Seiberg N 2004 Unitary and complex matrix models as 1D Type 0 strings Commun. Math. Phys. 252 275-323 (arXiv:hep-th/0309168)
29. Gross D J and Witten E 1980 Possible third order phase transition in the large N lattice gauge theory Phys. Rev. D 21 446-53
30. Semenoff G W and Szabo R J 1997 Fermionic matrix models Int. J. Mod. Phys. A 12 2135-292 (arXiv:hep-th/9605140)
31. Paniak L D and Szabo R J 2003 Open Wilson lines and group theory of noncommutative Yang-Mills theory in two dimensions J. High Energy Phys. JHEP05(2003)029 (arXiv:hep-th/0302162)
32. Paniak L D and Szabo R J 2005 Lectures on two-dimensional noncommutative gauge theory: 2. Quantization Lecture Notes Phys. 662 205-37 (arXiv:hep-th/0304268)
33. Szabo R J 2003 Quantum field theory on noncommutative spaces Phys. Rep. 378 207-99 (arXiv:hep-th/0109162)
34. Sutherland B 1971 Exact results for a quantum many-body problem in one dimension Phys. Rev. A 5 2019-21
35. Gorsky A and Nekrasov N A 1994 Hamiltonian systems of Calogero type and two-dimensional Yang-Mills theory Nucl. Phys. B 414 213-38 (arXiv:hep-th/ 9304047)
36. Minahan J A and Polychronakos A P 1994 Interacting fermion systems from two-dimensional QCD Phys. Lett. B 326 288-94 (arXiv:hep-th/9309044)
37. de Haro S 2005 Chern-Simons theory, 2D Yang-Mills, and Lie algebra wanderers Nucl. Phys. B 730 312-51 (arXiv:hep-th/0412110)
38. Andrews G E, Askey R and Roy R 1999 Special Functions (Cambridge: Cambridge University Press)
39. Koornwinder T H 2005 q-Special functions: an overview arXiv:math/0511148
40. de Haro S and Tierz M 2005 Discrete and oscillatory matrix models in Chern-Simons theory Nucl. Phys. B 731 225-41 (arXiv:hep-th/0501123)
41. Ramis J-P 1992 About the growth of entire functions solutions of linear algebraic q-difference equations Ann. Fac. Sci. Toulouse Math. 1 53-94
42. Gel'fand I M, Graev M I and Retakh V S 1998 General gamma functions, exponentials, and hypergeometric functions Russ. Math. Surv. 53 1-55
43. Ismail M E H, Stanton D and Viennot G 1987 The combinatorics of q-Hermite polynomials and the Askey-Wilson integral Eur. J. Comb. 8 379-92
44. Szeg G 1981 Orthogonal Polynomials (Providence, RI: American Mathematical Society)
45. Atakishiyev N M and Nagiyev Sh M 1994 On the Rogers-Szeg polynomials J. Phys. A: Math. Gen. 27 L611-5
46. Muttalib K A and Ismail M E H 1995 Impact of localization on Dyson's circular ensemble J. Phys. A: Math. Gen. 28 L541-8 (arXiv:cond-mat/9510005)
47. Morozov A Yu 2009 Unitary integrals and related matrix models arXiv:0906.3518 [hep-th]
48. Tierz M 2009 Chern-Simons theory, exactly solvable models and free fermions at finite temperature Mod. Phys. Lett. A 24 3157-71 (arXiv:0808.1079 [hep-th])
49. Polychronakos A P 2006 Physics and mathematics of Calogero particles J. Phys. A: Math. Gen. 39 12793-846 (arXiv:hep-th/0607033)
50. Haldane F D M 1988 Exact Jastrow-Gutzwiller resonating-valence-bond ground state of the spin-antiferromagnetic Heisenberg chain with exchange Phys. Rev. Lett. 60 635-8
51. Shastry B S 1988 Exact solution of an Heisenberg antiferromagnetic chain with long-ranged interactions Phys. Rev. Lett. 60 639-42
52. Sierra G and Cirac J I 2009 Infinite matrix product states, conformal field theory and the Haldane-Shastry model arXiv:0911.3029 [cond-mat.stat-mech]
53. Kapustin A, Willett B and Yaakov I 2009 Exact results for Wilson loops in superconformal Chern-Simons theories with matter arXiv:0909.4559 [hep-th]
54. Jeffrey L C 1992 Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation Commun. Math. Phys. 147 563-604
55. Olshanetsky M A and Perelomov A M 1983 Quantum integrable systems related to Lie algebras Phys. Rep. 94 313-404
56. Sinha S and Vafa C 2000 SO and Sp Chern-Simons at large N arXiv:hep-th/0012136
57. Füchs J 1995 Affine Lie Algebras and Quantum Groups: An Introduction, with Applications in Conformal Field Theory (Cambridge: Cambridge University Press)
58. Fradkin E S, Moreno E and Schaposnik F A 1993 Ground state wavefunctionals for 1 + 1-dimensional fermion field theories Nucl. Phys. B 392 667-99 (arXiv:hep-th/9207003)