Refined BPS state counting from nekrasov's formula and macdonald functions

International Journal of Modern Physics A

Volumn 24, Issue 12, 2009, Pages 2253-2306

  Awata, Hidetoshi ^a   Kanno, Hiroaki ^a  

^a NAGOYA UNIVERSITY   (Japan)

Author keywords

BPS state; Symmetric functions; Topological string

Indexed keywords

EID: 67549087964     PISSN: 0217751X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0217751X09043006     Document Type: Article

References (39)

1. N. Nekrasov, Adv. Theor. Math. Phys. 7, 831 (2003), arXiv:hep-th/0206161.
2. M. Aganagic, M. Mariño and C. Vafa, Commun. Math. Phys. 247, 467 (2004), arXiv:hep-th/0206164.
3. M. Aganagic, A. Klemm, M. Mariño and C. Vafa, Commun. Math. Phys. 254, 425 (2005), arXiv:hep-th/0305132.
4. S. Katz, A. Klemm and C. Vafa, Nucl. Phys. B 497, 173 (1997), arXiv:hepth/9609239.
5. S. Katz, P. Mayr and C. Vafa, Adv. Theor. Math. Phys. 1, 53 (1998), arXiv:hepth/9706110.
6. H. Nakajima and K. Yoshioka, Invent. Math. 162, 313 (2005), arXiv:math.AG/0306198.
7. A. Iqbal and A.-K. Kashani-Poor, Adv. Theor. Math. Phys. 7, 457 (2003), arXiv:hepth/0212279.
8. A. Iqbal and A.-K. Kashani-Poor, Adv. Theor. Math. Phys. 10, 1 (2006), arXiv:hepth/0306032.
9. T. Eguchi and H. Kanno, J. High Energy Phys. 0312, 006 (2003), arXiv:hepth/0310235.
10. T. Eguchi and H. Kanno, Phys. Lett. B 585, 163 (2004), arXiv:hep-th/0312234.
11. T. Hollowood, A. Iqbal and C. Vafa, J. High Energy Phys. 0803, 069 (2008), arXiv:hep-th/0310272.
12. J. Zhou, Curve counting and instanton counting, arXiv:math.AG/0311237.
13. A. Iqbal, C. Kozcaz and C. Vafa, The refined topological vertex, arXiv:hepth/0701156.
14. H. Awata and H. Kanno, J. High Energy Phys. 0505, 039 (2005), arXiv:hepth/0502061.
15. I. G. Macdonald, Symmetric Functions and Hall Polynomials, 2nd edn. (Oxford UniversityPress, 1995).
16. M. Taki, J. High Energy Phys. 0803, 048 (2008), arXiv:0710.1776[hep-th].
17. A. Okounkov, N. Reshetikhin and C. Vafa, Quantum Calabi-Yau and classical crystals,arXiv:hep-th/0309208.
18. A. Iqbal, C. Kozcaz and K. Shabbir, Refined topological vertex, cylindric partitions and U(1), adjoint theory, arXiv:0803.2260.
19. R. Gopakumar and C. Vafa, M theory and topological strings I, arXiv:hep-th/9809187.
20. R. Gopakumar and C. Vafa, M theory and topological strings II, arXiv:hepth/9812127.
21. S. Katz, A. Klemm and C. Vafa, Adv. Theor. Math. Phys. 3, 1445 (1999), arXiv:hepth/9910181.
22. P. Peng, A simple proof of Gopakumar-Vafa conjecture for local toric Calabi-Yau manifolds, arXiv:math.AG/0410540.
23. Y. Konishi, Publ. Res. Inst. Math. Sci. 42, 173 (2006), arXiv:math.AG/0411357.
24. Y. Konishi, Publ. Res. Inst. Math. Sci. 42, 605 (2006), arXiv:math.AG/0504188.
25. H. Awata, H. Kubo, S. Odake and J. Shiraishi, Commun. Math. Phys. 179, 401 (1996), arXiv:q-alg/9508011.
26. H. Nakajima and K. Yoshioka, Instanton counting on blowup II. K-theoretic partition function, arXiv:math.AG/0505553.
27. L. Göttsche, H. Nakajima and K. Yoshioka, K-theoretic Donaldson invariants via instanton counting, arXiv:math.AG/0611945.
28. S. Gukov, A. Schwarz and C. Vafa, Lett. Math. Phys. 74, 53 (2005), arXiv:hepth/0412243.
29. S. Gukov, A. Iqbal, C. Kozcaz and C. Vafa, Link homologies and the refined topological vertex, arXiv:0705.1368.
30. Y. Tachikawa, J. High Energy Phys. 0402, 050 (2004), arXiv:hep-th/0401184.
31. N. Nekrasov and A. Okounkov, Seiberg-Witten theory and random partitions, in The Unity of Mathematics, Progr. Math., Vol. 244, eds. P. Etingof, V. Retakh and I. M. Singer (Birkḧauser, 2005), p. 525, arXiv:hep-th/0306238.
32. A. Iqbal and A.-K. Kashani-Poor, Adv. Theor. Math. Phys. 10, 317 (2006), arXiv:hepth/0410174.
33. H. Awata, S. Odake and J. Shiraishi, Commun. Math. Phys. 179, 647 (1996), arXiv:qalg/9506006.
34. Y. Konishi and S. Minabe, Int. J. Math. 19, 27 (2008), arXiv:math.AG/0601352.
35. J. Li, K. Liu and J. Zhou, Topological string partition functions as equivariant indices, arXiv:math.AG/0412089.
36. R. Poghossian and M. Samsonyan, Instantons and the 5D U(1) gauge theory with extra adjoint, arXiv:0804.3564.
37. I. Cherednik, Ann. Math. 141, 191 (1995).
38. A. N. Kirillov and M. Noumi, Affine Hecke algebras and raising operators for Macdonald polynomials, arXiv:q-alg/9605004.
39. M. Taki, Flop invariance of refined topological vertex and link homologies, arXiv:0805.0336.