Chern-Simons theory on L (p, q) lens spaces and Gopakumar-Vafa duality

Journal of Geometry and Physics

Volumn 60, Issue 3, 2010, Pages 417-429

  Brini, Andrea ^a,b   Griguolo, Luca ^c,d   Seminara, Domenico ^e,f   Tanzini, Alessandro ^a,b  

^a SISSA   (Italy)

^b SEZIONE DI TRIESTE   (Italy)

^c UNIVERSITY OF PARMA   (Italy)

^d INFN SEZIONE DI ROMA   (Italy)

^e UNIVERSITY OF FLORENCE   (Italy)

^f INFN SEZIONE DI FIRENZE   (Italy)

Author keywords

Chern Simons theory; Geometric transitions; Gopakumar Vafa; Large N duality; Open closed duality; Random matrices; Topological strings

Indexed keywords

EID: 75949097918     PISSN: 03930440     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.geomphys.2009.11.006     Document Type: Article

References (28)

1. Witten E. Quantum field theory and the Jones polynomial. Comm. Math. Phys. 121 (1989) 351
2. Gopakumar R., and Vafa C. On the gauge theory/geometry correspondence. Adv. Theor. Math. Phys. 3 (1999) 1415 [arXiv:hep-th/9811131]
3. 't Hooft G. A planar diagram theory for strong interactions. Nuclear Phys. B 72 (1974) 461
4. A. Grassi, M. Rossi, Large N dualities and transitions in geometry, arXiv:math/0209044
5. Auckly D., and Koshkin S. Introduction to the Gopakumar-Vafa large N duality. Geom. Topol. Monog. 8 (2006) 195-456 [arXiv:math/0701568]
6. Rossi M. Geometric transitions. J. Geom. Phys. 56 (2006) 1940 [arXiv:math/0412514]
7. Witten E. Chern-Simons gauge theory as a string theory. Progr. Math. 133 (1995) 637 [arXiv:hep-th/9207094]
8. Halmagyi N., Okuda T., and Yasnov V. Large N duality, lens spaces and the Chern-Simons matrix model. J. High Energy Phys. 0404 (2004) 014 [arXiv:hep-th/0312145]
9. N. Halmagyi, V. Yasnov, The spectral curve of the lens space matrix model arXiv:hep-th/0311117
10. Marino M. Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants. Comm. Math. Phys. 253 (2004) 25 [arXiv:hep-th/0207096]
11. Aganagic M., Klemm A., Marino M., and Vafa C. Matrix model as a mirror of Chern-Simons theory. J. High Energy Phys. 0402 010 (2004) [arXiv:hep-th/0211098]
12. Givental A.B. A mirror theorem for toric complete intersections. Topological Field Theory, Primitive Forms and Related Topics (Kyoto, 1996). Progr. Math. vol. 160 (1998), Birkhäuser Boston, Boston, MA 141-175
13. Lian B.H., Liu K., and Yau S.T. Mirror principle I. Asian J. Math. 1 (1997) 729-763
14. Elezi A. Mirror symmetry for concavex vector bundles on projective spaces. Int. J. Math. Math. Sci. (2003) 159-197
15. V. Bouchard, A. Klemm, M. Marino, S. Pasquetti, Remodeling the B-model, arXiv:0709.1453 [hep-th]
16. B. Eynard, Large N expansion of convergent matrix integrals, holomorphic anomalies, and background independence, arXiv:0802.1788 [math-ph]
17. B. Eynard, M. Marino, A holomorphic and background independent partition function for matrix models and topological strings, arXiv:0810.4273 [hep-th]
18. M. Marino, Nonperturbative effects and nonperturbative definitions in matrix models and topological strings, arXiv:0805.3033 [hep-th]
19. M. Marino, R. Schiappa, M. Weiss, Nonperturbative effects and the large-order behavior of matrix models and topological strings, arXiv:0711.1954 [hep-th]
20. Stiefel E. Richtungsfelder und Fernparallelismus in n-dimensionalen Mannigfaltigkeiten. Comment. Math. Helv. 8 1 (1935) 305-353
21. Fulton W. Introduction to toric varieties. The William H. Roever Lectures in Geometry. Annals of Mathematics Studies vol. 131 (1993), Princeton University Press
22. K. Hori, C. Vafa, Mirror symmetry, arXiv:hep-th/0002222
23. B. Feng, Y.H. He, K.D. Kennaway, C. Vafa, Dimer models from mirror symmetry and quivering amoebae, arXiv:hep-th/0511287
24. S. Garoufalidis, M. Marino, On Chern-Simons matrix models, arXiv:math/0601390
25. Dolivet Y., and Tierz M. Chern-Simons matrix models and Stieltjes-Wigert polynomials. J. Math. Phys. 48 (2007) 023507 [arXiv:hep-th/0609167]
26. Hansen S.K., and Takata T. Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras. J. Knot Theory Ramifications 13 (2004) [arXiv:math/0209403]
27. Griguolo L., Seminara D., Szabo R.J., and Tanzini A. Nuclear Phys. B 772 (2007) 1 [arXiv:hep-th/0610155]
28. Itzykson C., and Zuber J.B. The planar approximation. 2. J. Math. Phys. 21 (1980) 411