Hilbert schemes, separated variables, and D-Branes

Communications in Mathematical Physics

Volumn 222, Issue 2, 2001, Pages 299-318

  Gorsky, A ^a,d   Nekrasov, N ^b,d,e   Rubtsov, V ^a,c,d  

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

^b HARVARD UNIVERSITY   (United States)

^c UNIVERSITÉ D'ANGERS   (France)

^d Institut Mittag Leffler   (Sweden)

^e INSTITUT DES HAUTES ÉTUDES SCIENTIFIQUES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035615603     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200100503     Document Type: Article

References (54)

1. 1. Sklyanin, E.: Separation of variables. New trends. solv-int/9505035
2. 2. Sklyanin, E.: Separation of variables in the classical integrable SL(3) magnetic chain. Commun. Math. Phys. 150, 181-191 (1992)
3. 3. Flaschka, H. and McLaughlin, D.W.: Progr. Theor. Phys. 55, 438-456 (1976); Gelfand, I.M. and Dikii, L.A.: Func. Anal. Appl. 13, 8-20 (1979); Novikov, S.P. and Veselov, A.P.: Proc. Steklov Inst. Math. 3, 53-65 (1985)
4. 3. Flaschka, H. and McLaughlin, D.W.: Progr. Theor. Phys. 55, 438-456 (1976); Gelfand, I.M. and Dikii, L.A.: Func. Anal. Appl. 13, 8-20 (1979); Novikov, S.P. and Veselov, A.P.: Proc. Steklov Inst. Math. 3, 53-65 (1985)
5. 3. Flaschka, H. and McLaughlin, D.W.: Progr. Theor. Phys. 55, 438-456 (1976); Gelfand, I.M. and Dikii, L.A.: Func. Anal. Appl. 13, 8-20 (1979); Novikov, S.P. and Veselov, A.P.: Proc. Steklov Inst. Math. 3, 53-65 (1985)
6. 4. Krichever, I., Phong, D.H.: On the integrable geometry of soliton equations and N=2 supersymmetric gauge theories. hep-th/9604199, J. Diff. Geom. 45, 349-389 (1997)
7. 5. Hitchin, N.: Stable bundles and integrable systems. Duke. Math. J. 54, 91-114 (1987)
8. 6. Donagi, R., Ein, L., Lazarsfeld, R.: alg-geom/9504017; Nilpotent cones and sheaves on K3 surfaces. Birational algebraic geometry (Baltimore, MD, 1996), Contemp. Math., 207, Providence, RI: Am. Math. Soc. 1997, pp. 51-61
9. 7. Nekrasov, N.: Holomorphic bundles and many-body systems. hep-th/9503157, Commun. Math. Phys. 180, 587 (1996)
10. 8. Enriquez, B., Rubtsov, V.: Hitchin systems, higher Gaudin operators and r-matrices. alg-geom/9503010, Math. Res. Lett. 3, no. 3, 343-357 (1996)
11. 9. Hurtubise, J.: Integrable systems and algebraic surfaces. Duke. Math. J. 83, 19-50 (1996)
12. 10. Nakajima, H.: Jack polynomials and Hilbert schemes of points on surfaces. aig-geom/9610021
13. 11. Wilson, G.: Collisions of Calogero-Moser particles and an adelic Grassmanian. Inv. Math. 133, no. 1, 1-41 (1998)
14. 12. Beauville, A.: Variétés Kahleriennes dont la première classe de Chern est nulle. J. Diff. Geom. 18, no. 4, 755-782 (1983)
15. 13. Gorsky, A., Nekrasov, N.: Hamiltonian systems of Calogero type and Two Dimensional Yang-Mills Theory. Nucl. Phys. B 414, 213-238(1994)
16. 14. Witten, E.: Bound States of Strings and p-Branes. hep-th/9510135, Nucl. Phys. B 460, 335-350 (1996)
17. 15. Vafa, C.: Instantons on D branes. hep-th/9512078, Nucl. Phys. B 463, 435-442 (1996)
18. 16. Garnier, R.: Sur une classe de systèmes différentiels Abeliéns déduits de la théorie des équations linéares. Rend. del Circ. Matematice Di Palermo 43, vol. 4 (1919)
19. 17. Gaudin, M.: J. Physique, 37, 1087-1098 (1976)
20. 18. Sutherland, B.: Phys. Rev. A 5, 1372-13 (1972)
21. 19. Nakajima, H.: Lectures on Hilbert schemes of points on surfaces. H. Nakajima's homepage
22. 4 and six dimensional (2, 0) superconformal theory. hep-th/9802068, Commun. Math. Phys. 198, 689-703 (1998)
23. 21. Calogero, F.: J. Math. Phys. 12, 419 (1971)
24. 22. Airault, H., McKean, H., Moser, J.: Rational and elliptic solutions of the KdV equation and a related many-body problem. Comm. Pure. Appl. Math. 30, no. 1, 95-148 (1977)
25. 23. Krichever, I.: Funk. Anal. and Appl. 12 1, 76-78 (1978); 14, 282-290 (1980)
26. 23. Krichever, I.: Funk. Anal. and Appl. 12 1, 76-78 (1978); 14, 282-290 (1980)
27. 24. Kazhdan, D., Kostant, B. and Sternberg, S.: Comm. on Pure and Appl. Math. vol. XXXI, 481-507 (1978)
28. 25. Olshanetsky, M., Perelomov, A.: Phys. Rep. 71, 313 (1981)
29. 26. Ruijsenaars, S.: Commun. Math. Phys. 110, 191-213 (1987)
30. 27. Ruijsenaars, S.N.M., Schneider, H.: Ann. of Physics 170, 370-405 (1986)
31. 28. Moser, J.: Adv. Math. 16, 197-220 (1975)
32. 29. Gorsky, A., Nekrasov, N.: Relativistic Calogero-Moser model as gauged WZW theory. Nucl. Phys. B 436, 582-608 (1995)
33. 30. Kronheimer, P.: The construction of ALE spaces as hyper-kahler quotients. J. Diff. Geom. 28, 665 (1989)
34. 31. Kronheimer, P. and Nakajima, H.: Yang-Mills instantons on ALE gravitational instantons. Math. Ann. 288, 263 (1990)
35. 32. Nakajima, H.: Homology of moduli spaces of instantons on ALE Spaces, I. J. Diff. Geom. 40, 105 (1990); Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. Preprint; Gauge theory on resolutions of simple singularities and affine Lie algebras. Preprint
36. 32. Nakajima, H.: Homology of moduli spaces of instantons on ALE Spaces, I. J. Diff. Geom. 40, 105 (1990); Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. Preprint; Gauge theory on resolutions of simple singularities and affine Lie algebras. Preprint
37. 32. Nakajima, H.: Homology of moduli spaces of instantons on ALE Spaces, I. J. Diff. Geom. 40, 105 (1990); Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. Preprint; Gauge theory on resolutions of simple singularities and affine Lie algebras. Preprint
38. 33. Hitchin, N.: The self-duality equations on a Riemann surface. Proc. London Math. Soc. 55, 59-126 (1987)
39. 34. Gorsky, A., Nekrasov, N.: Elliptic Calogero-Moser System from Two Dimensional Current Algebra. hepth/9401021
40. 35. Markman, E.: Spectral curves and integrable systems. Compositio Math. 93, no. 3, 255-290 (1994)
41. 36. Kapustin, A., Sethi, S.: The Higgs Branch of Impurity Theories. hep-th/9804027, Adv. Theor. Math. Phys. 2, 571-591 (1998)
42. 37. Taylor, W.: D-Brane Field Theory on a Compact Space. hep-th/9611042, Phys. Lett. B 394, 283-287 (1997)
43. 38. Bochicchio, M.: The large-N limit of QCD and the collective field of the Hitchin fibration. hep-th/9810015
44. 39. Beauville, A.: Systèmes Hamiltoniens complètement intègrables associés aux surfaces K3. In: Problems in the theory of surfaces and their classification (Cortona, 1988), Sympos. Math. XXXII, London: Academic Press, 1991, pp. 25-31
45. 40. Beauville, A.: Counting rational curves on K3 surfaces. alg-geom/9701019
46. 41. Bershadsky, M., Vafa, C., Sadov, V.: D-branes and topological theories. Nucl. Phys. B 463, 420-434 (1996)
47. 42. Yau, S.-T., Zaslow, E.: BPS States, string duality and nodal curves on K3. hep-th/9512121
48. 43. Altman, A., Kleiman, S.: Compactifying the Picard scheme. Adv. in Math. 35, 50-112 (1980)
49. 44. Mukai, S.: Symplectic structure of the moduli space on a abelian or K3 surface. Invent. Math. 83, 101-116 (1984)
50. 45. Dijkgraaf, R.: Instanton Strings and HyperKähler Geometry. hep-th/9810210
51. 46. Beilinson, A., Drinfeld, V.: Quantization of Hitchin's fibration and Langlands' program. In: Algebraic and geometric methods in mathematical physics (Kaciveli, 1993), Math. Phys. Stud. 19, Dordrecht: Kluwer Acad. Publ., 1996, pp. 3-7
52. 47. Feigin, B., Frenkel, E., Reshetikhin, N.: Gaudin Model, Critical Level and Bethe Ansatz. Commun. Math. Phys. 166, 27-62 (1995)
53. 48. Frenkel, E.: Affine algebras, Langlands duality and Bethe ansatz. In: XIth International Congress of Mathematical Physics (Paris, 1994), Cambridge. MA: Internat. Press. 1995, pp. 606-642, q-alg/9506003
54. 2-Calogero-Gaudin system. Compositio Math. 110, no. 1, 1-16 (1998), q-alg/9605030