Topological expansion of the β-ensemble model and quantum algebraic geometry in the sectorwise approach

Theoretical and Mathematical Physics

Volumn 166, Issue 2, 2011, Pages 141-185

  Chekhov, L O ^a,b,c   Eynard, B ^d   Marchal, O ^d  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^c Laboratoire Poncelet   (Russian Federation)

^d Centre National de la Recherche Scientifique   (France)

Author keywords

Bergman kernel; correlation function; flat coordinates; Riccati equation; Riemann identity; Schr dinger equation

Indexed keywords

EID: 79953677510     PISSN: 00405779     EISSN: 15739333     Source Type: Journal    
DOI: 10.1007/s11232-011-0012-3     Document Type: Article

References (18)

1. L. O. Chekhov, B. Eynard, and O. Marchal, "Topological expansion of the Bethe ansatz, and quantum algebraic geometry," arXiv: 0911. 1664v2 [math-ph] (2009).
2. B. Eynard, JHEP, 0411, 031 (2004); arXiv: hep-th/0407261v1 (2004).
3. B. Eynard and N. Orantin, Comm. Number Theory Phys., 1, 347-452 (2007); arXiv: math-ph/0702045v4 (2007).
4. L. Chekhov and B. Eynard, JHEP, 0603, 014 (2006); arXiv: hep-th/0504116v1 (2005).
5. L. Chekhov, B. Eynard, and N. Orantin, JHEP, 0612, 053 (2006); arXiv: math-ph/0603003v2 (2006).
6. B. Eynard and A. Prats Ferrer, arXiv: 0805. 1368v2 [math-ph] JHEP, 0907, 096 (2008).
7. M. L. Mehta, Random Matrices (Pure Appl. Math. Ser., Vol. 142), Elsevier, Amsterdam (2004).
8. L. Chekhov and B. Eynard, JHEP, 0612, 026 (2006); arXiv: math-ph/0604014v1 (2006).
9. I. Dumitriu and A. Edelman, J. Math. Phys., 43, 5830-5847 (2002); arXiv: math-ph/0206043v1 (2002).
10. B. Eynard, J. Phys. A, 34, 7591-7605 (2001); arXiv: cond-mat/0012046v1 (2000).
11. L. F. Alday, D. Gaiotto, and Y. Tachikawa, Lett. Math. Phys., 91, 167-197 (2010); arXiv: 0906. 3219v2 [hep-th] (2009).
12. A. Nekrasov, Adv. Theor. Math. Phys., 7, 831-864 (2003); arXiv: hep-th/0306211v1 (2003).
13. A. Mironov and A. Morozov, Phys. Lett. B, 680, 188-194 (2009); arXiv: 0908. 2190v1 [hep-th] (2009); A. Marshakov, A. Mironov, and A. Morozov, Phys. Lett. B, 682, 125-129 (2009); arXiv: 0909. 2052v1 [hep-th] (2009); JHEP, 0911, 048 (2009); arXiv: 0909. 3338v3 [hep-th] (2009).
14. T. Eguchi and K. Maruyoshi, JHEP, 1002, 022 (2010); arXiv: 0911. 4797v3 [hep-th] (2009).
15. B. Eynard and O. Marchal, JHEP, 0903, 094 (2009); arXiv: 0809. 3367v1 [math-ph] (2008).
16. I. M. Krichever, Comm. Pure Appl. Math., 47, 437-475 (1994); arXiv: hep-th/9205110v1 (1992).
17. I. M. Gel'fand and L. A. Dikii, Funct. Anal. Appl., 13, No. 1, 6-15 (1979).
18. O. Babelon and D. Talalaev, J. Stat. Mech. Theory Exp., 0706, P06013 (2007); arXiv: hep-th/0703124v1 (2007).