Chern-Simons theory, 2d Yang-Mills, and Lie algebra wanderers

Nuclear Physics B

Volumn 730, Issue 3, 2005, Pages 312-351

  de Haro, Sebastian ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27944476710     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nuclphysb.2005.09.009     Document Type: Article

References (64)

1. G. 't Hooft A planar diagram theory for strong interactions Nucl. Phys. B 72 1974 461
2. J.M. Maldacena The large N limit of superconformal field theories and supergravity Adv. Theor. Math. Phys. 2 1998 231 hep-th/9711200
3. J.M. Maldacena Int. J. Theor. Phys. 38 (1999) 1113, hep-th/9711200.
4. R. Gopakumar C. Vafa On the gauge theory/geometry correspondence Adv. Theor. Math. Phys. 3 1999 1415 hep-th/9811131
5. D.J. Gross Two-dimensional QCD as a string theory Nucl. Phys. B 400 1993 161 hep-th/9212149
6. A.A. Migdal Sov. Phys. JETP 42 1975 413
7. A.A. Migdal Zh. Eksp. Teor. Fiz. 69 1975 810
8. C. Vafa Two-dimensional Yang-Mills, black holes and topological strings hep-th/0406058
9. S. de Haro Chern-Simons theory in lens spaces from 2d Yang-Mills on the cylinder hep-th/0407139
10. M. Aganagic H. Ooguri N. Saulina C. Vafa Black holes, q-deformed 2d Yang-Mills, and nonperturbative topological strings hep-th/0411280
11. S. de Haro M. Tierz Brownian motion, Chern-Simons theory, and 2d Yang-Mills hep-th/0406093
12. A. Okounkov N. Reshetikhin C. Vafa Quantum Calabi-Yau and classical crystals hep-th/0309208
13. T. Matsuo S. Matsuura K. Ohta Large N limit of 2D Yang-Mills theory and instanton counting hep-th/0406191
14. E. Buffenoir P. Roche Link invariants and combinatorial quantization of Hamiltonian Chern-Simons theory Commun. Math. Phys. 181 1996 331-365 q-alg/9507001
15. E. Witten On quantum gauge theories in two-dimensions Commun. Math. Phys. 141 1991 153
16. M. Blau G. Thompson Quantum Yang-Mills theory on arbitrary surfaces Int. J. Mod. Phys. A 7 1992 3781
17. M. Blau G. Thompson Derivation of the Verlinde formula from Chern-Simons theory and the G/G model Nucl. Phys. B 408 1993 345 hep-th/9305010
18. M. Blau G. Thompson Lectures on 2d gauge theories: Topological aspects and path integral techniques hep-th/9310144
19. M. Blau G. Thompson Localization and diagonalization: A review of functional integral techniques for low-dimensional gauge theories and topological field theories J. Math. Phys. 36 1995 2192 hep-th/9501075
20. M. Polyak N. Reshetikhin On 2d Yang-Mills theory and invariants of links Deformation Theory and Symplectic Geometry, Ascona Mathematical Physics Studies vol. 20 1996 Kluwer Academic Dordrecht 223-248
21. A. Gorsky N. Nekrasov Hamiltonian systems of Calogero type and two-dimensional Yang-Mills theory Nucl. Phys. B 414 1994 213 hep-th/ 9304047
22. S. Karlin J.L. McGregor The differential equations of birth-and-death processes, and the Stieltjes moment problem Trans. Amer. Math. Soc. 85 1957 489-546
23. S. Karlin J.L. McGregor Coincidence probabilities Pacific J. Math. 9 1959 1141-1164
24. M. Kac Random walk and the theory of Brownian motion Amer. Math. Monthly 54 1947 369-391
25. M.E. Fisher Walks, walls, wetting, and melting J. Stat. Phys. 34 1984 667
26. D.A. Huse M.E. Fisher Commensurate melting, domain walls, and dislocation Phys. Rev. B 29 1984 239
27. S. Bochner Sturm-Liouville and heat equations whose eigenvalues are ultraspherical polynomials or associated Bessel functions in: R.C. Gunning (Ed.) Collected Papers of Salomon Bochner 1991 American Mathematical Society Providence
28. M. Tierz Soft matrix models and Chern-Simons partition functions Mod. Phys. Lett. A 19 2004 1365 hep-th/0212128
29. C. Itzykson J.B. Zuber The planar approximation. 2 J. Math. Phys. 21 1980 411
30. E. Witten Quantum field theory and the Jones polynomial Commun. Math. Phys. 121 1989 351
31. K. Murasugi Knot Theory and Its Applications 1996 Birkhäuser Boston
32. W.B.R. Lickorish An Introduction to Knot Theory 1997 Springer-Verlag New York
33. L.C. Jeffrey Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation Commun. Math. Phys. 147 1992 563
34. L. Rozansky A Contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds. 1 Commun. Math. Phys. 175 1996 275 hep-th/9401061
35. L. Rozansky A Contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds. 2 Commun. Math. Phys. 175 1996 297 hep-th/9403021
36. M. Mariño Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants hep-th/0207096
37. D.J. Grabiner Brownian motion in a Weyl chamber, non-colliding particles, and random matrices Ann. Inst. H. Poincaré Probab. Statist. 35 1999 177-204 math.RT/9708207
38. W. Fulton J. Harris Representation Theory: A First Course 1991 Springer-Verlag New York
39. S. Sinha C. Vafa SO and Sp Chern-Simons at large N hep-th/0012136
40. I.M. Gessel D. Zeilberger Random walk in a Weyl chamber Proc. Amer. Math. Soc. 115 1992 27
41. M. Aganagic A. Klemm M. Mariño C. Vafa Matrix model as a mirror of Chern-Simons theory JHEP 0402 2004 010 hep-th/0211098
42. S. de Haro, M. Tierz, in preparation
43. S. Elitzur G.W. Moore A. Schwimmer N. Seiberg Remarks on the canonical quantization of the Chern-Simons-Witten theory Nucl. Phys. B 326 1989 108
44. P. Candelas X.C. de la Ossa Comments on conifolds Nucl. Phys. B 342 1990 246
45. M. Aganagic C. Vafa Mirror symmetry, D-branes and counting holomorphic discs hep-th/0012041
46. R. Dijkgraaf C. Vafa Matrix models, topological strings, and supersymmetric gauge theories Nucl. Phys. B 644 2002 3 hep-th/0206255
47. J. de Boer S. de Haro The off-shell M5-brane and nonperturbative gauge theory Nucl. Phys. B 696 2004 174 hep-th/0403035
48. M. Aganagic A. Klemm M. Mariño C. Vafa Topological strings and integrable hierarchies hep-th/0312085
49. R. Dijkgraaf A. Sinkovics M. Temurhan Universal correlators from geometry JHEP 0411 2004 012 hep-th/0406247
50. G. Szegö Orthogonal Polynomials 1939 American Mathematical Society Providence
51. M.L. Mehta Random Matrices second ed. 1990 Academic Press San Diego
52. P. Zinn-Justin Universality of correlation functions of Hermitian random matrices in an external field Commun. Math. Phys. 194 1998 631-650 cond-math/9705044
53. P. Zinn-Justin Random Hermitian matrices in an external field Nucl. Phys. B 497 1997 725 cond-mat/9703033
54. M. Katori H. Tanemura Scaling limit of vicious walks and two-matrix model Phys. Rev. E 66 2002 011105 cond-mat/0203549
55. M.L. Mehta A method of integration over matrix variables Commun. Math. Phys. 79 1981 327
56. V.A. Kazakov A. Marshakov Complex curve of the two matrix model and its tau-function J. Phys. A 36 2003 3107 hep-th/0211236
57. J. Johansson Universality of the local spacing distribution in certain ensembles of Hermitian Wigner matrices Commun. Math. Phys. 215 2001 683-705 math-ph/0006020
58. M. Bertola B. Eynard Mixed correlation functions of the two-matrix model J. Phys. A 36 2003 7733 hep-th/0303161
59. S. de Haro, in preparation
60. T. Okuda Derivation of Calabi-Yau crystals from Chern-Simons gauge theory hep-th/0409270
61. S.R. Das G. Mandal S.R. Wadia Mod. Phys. Lett. A 4 1989 745
62. G. Parisi N. Sourlas Random magnetic fields, supersymmetry and negative dimensions Phys. Rev. Lett. 43 1979 744
63. G. Parisi N. Sourlas Supersymmetric field theories and stochastic differential equations Nucl. Phys. B 206 1982 321
64. P. Di Francesco P. Mathieu D. Sénéchal Conformal Field Theory 1997 Springer-Verlag New York