Chern-Simons theory in lens spaces from 2d Yang-Mills on the cylinder

Journal of High Energy Physics

Volumn 8, Issue 8, 2004, Pages 1097-1118

  De Haro, Sebastian ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

Chern Simons Theories; Field Theories in Lower Dimensions; Topological Strings

Indexed keywords

EID: 23044435326     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. A.A. Migdal, Recursion equations in gauge field theories, Sov. Phys. JETP 42 (1975) 413.
2. D.J. Gross, Two-dimensional QCD as a string theory, Nucl. Phys. B 400 (1993) 161 [hep-th/9212149].
3. S. Cordes, G.W. Moore and S. Ramgoolam, Lectures on 2-d Yang-Mills theory, equivariant cohomology and topological field theories, Nucl. Phys. 41 (Proc. Suppl.) (1995) 184 [hep-th/9411210].
4. G. 't Hooft, A planar diagram theory for strong interactions, Nucl. Phys. B 72 (1974) 461.
5. 9We actually use the notation in [37].
6. D.J. Gross and I.W. Taylor, Two-dimensional QCD is a string theory, Nucl. Phys. B 400 (1993) 181 [hep-th/9301068].
7. R. Dijkgraaf, Chiral deformations of conformal field theories, Nucl. Phys. B 493 (1997) 588 [hep-th/9609022].
8. N.A. Nekrasov, Seiberg-Witten prepotential from instanton counting, hep-th/0306211;
9. N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, hep-th/0306238.
10. S. de Haro and M. Tierz, Brownian motion, Chern-Simons theory and 2D Yang-Mills, hep-th/0406093.
11. T. Matsuo, S. Matsuura and K. Ohta, Large-N limit of 2D Yang-Mills theory and instanton counting, hep-th/0406191.
12. E. Witten, On quantum gauge theories in two-dimensions, Commun. Math. Phys. 141 (1991) 153.
13. E. Witten, Two-dimensional gauge theories revisited, J. Geom. Phys. 9 (1992) 303 [hep-th/9204083].
14. R. Dijkgraaf and C. Vafa, N = 1 supersymmetry, deconstruction and bosonic gauge theories, hep-th/0302011.
15. I.B. Frenkel, Orbital theory for affine Lie algebras, Invent. Math. 77 (1984) 301.
16. H.D. Fegan, The heat equation on a compact Lie group, Trans. Amer. Math. Society 246 (1978) 339.
17. M.R. Douglas, Conformal field theory techniques in large-N Yang-Mills theory, hep-th/9311130.
18. R.E. Rudd, The string partition function for QCD on the torus, hep-th/9407176.
19. M. Blau and G. Thompson, Quantum Yang-Mills theory on arbitrary surfaces, Int. J. Mod. Phys. A 7 (1992) 3781;
20. M. Blau and 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];
21. M. Blau and G. Thompson, Lectures on 2-D gauge theories: topological aspects and path integral techniques, hep-th/9310144;
22. 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].
23. D.J. Gross and A. Matytsin, Some properties of large-N two-dimensional Yang-Mills theory, Nucl. Phys. B 437 (1995) 541 [hep-th/9410054].
24. S. Zelditch, Macdonald's identities and the large-N limit of YM(2) on the cylinder, Commun. Math. Phys. 245 (2004) 611 [hep-th/0305218].
25. M.E. Fisher, Walks, walls, wetting, and melting, J. Stat. Phys. 34 (1984) 667;
26. D.A. Huse and M.E. Fisher, Commesurate melting, domain walls, and dislocation, Phys. Rev. D 29 (1984) 239.
27. I.M. Gessel and D. Zeilberger, Random walk in a weyl chamber, Proc. Amer. Math. Soc. 115 (1992) 27.
28. D.J. Grabiner, Brownian motion in a weyl chamber, non-colliding particles, and random matrices, Annales de l'I. H. P. Probabilites et Statistiques 35 (1999) 177-204 [math.RT/9708207].
29. M. Filaseta, A new method for solving a class of ballot problems, J. Combin. Theory, Series A 39 (1985) 102.
30. D.G. Hobson and W. Werner, Non-Colliding brownian Motions on the circle, Bull. London Math. Soc. 28 (1996) 643
31. V. Kac, Infinite dimensional Lie algebras, Cambridge University Press, Cambridge 1990.
32. P. Di Francesco, P. Mathieu and D. Sénéchal, Conformal field theory, Springer-Verlag, New York 1996.
33. E. Witten, Quantum field theory and the jones polynomial, Commun. Math. Phys. 121 (1989) 351.
34. L.C. Jeffrey, Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation, Commun. Math. Phys. 147 (1992) 563.
35. L. Rozansky, A large k asymptotics of Witten's invariant of seifert manifolds, Commun. Math. Phys. 171 (1995) 279 [hep-th/9303099];
36. L. Rozansky, A contribution to the trivial connection to jones polynomial and Witten's invariant of 3-d manifolds, 1, Commun. Math. Phys. 175 (1996) 275 [hep-th/9401061].
37. M. Marino, Chern-Simons theory, matrix integrals and perturbative three-manifold invariants, hep-th/0207096.
38. M. Aganagic, A. Klemm, M. Marino and C. Vafa, Matrix model as a mirror of Chern-Simons theory, J. High Energy Phys. 02 (2004) 010 [hep-th/0211098].
39. N. Halmagyi, T. Okuda and V. Yasnov, Large-N duality, lens spaces and the Chern-Simons matrix model, J. High Energy Phys. 04 (2004) 014 [hep-th/0312145];
40. N. Halmagyi and V. Yasnov, The spectral curve of the lens space matrix model, hep-th/0311117.
41. M. Atiyah, The logarithm of the dedekind η-function, Math. Ann. 278 (1987) 335.
42. E. Verlinde, Fusion rules and modular transformations in 2-d conformal field theory, Nucl. Phys. B 300 (1988) 360.
43. R. Dijkgraaf, A. Sinkovics and M. Temurhan, Universal correlators from geometry, hep-th/0406247.
44. E. Elizalde, S.D. Odintsov, A. Romeo, A.A. Bytsenk and S. Zerbini, Zeta regularization techniques with applications, World Scientific, Singapore 1994.
45. D. Mumford, Tata Lectures on Theta I, Birkhäuser, Boston 1983.