Integrating over Higgs branches

Communications in Mathematical Physics

Volumn 209, Issue 1, 2000, Pages 97-121

  Moore, Gregory ^a   Nekrasov, Nikita ^b,c   Shatashvili, Samson ^a,d  

^a Yale University   (United States)

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

^c HARVARD UNIVERSITY   (United States)

^d STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034364849     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00005525     Document Type: Article

References (43)

1. 1. Vafa, C., Witten, E.: A strong coupling test of S-duality. Nucl. Phys. B 431, 3-77 (1994)
2. 2. Nakajima, H.: Homology of moduli spaces of instantons on ALE Spaces. I. J. Diff. Geom. 40, (1990) 105; Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. Duke. Math. J. 76, (1994) 365-416; Gauge theory on resolutions of simple singularities and affine Lie algebras. Inter. Math. Res. Notices 61-74 (1994)
3. 2. Nakajima, H.: Homology of moduli spaces of instantons on ALE Spaces. I. J. Diff. Geom. 40, (1990) 105; Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. Duke. Math. J. 76, (1994) 365-416; Gauge theory on resolutions of simple singularities and affine Lie algebras. Inter. Math. Res. Notices 61-74 (1994)
4. 2. Nakajima, H.: Homology of moduli spaces of instantons on ALE Spaces. I. J. Diff. Geom. 40, (1990) 105; Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras. Duke. Math. J. 76, (1994) 365-416; Gauge theory on resolutions of simple singularities and affine Lie algebras. Inter. Math. Res. Notices 61-74 (1994)
5. 3. Grojnowski, I.: Instantons and affine algebras I: The Hubert scheme and vertex operators. alg-geom/9506020
6. 4. Losev, A., Moore, G., Nekrasov, N., Shatashvili, S.: Four-Dimensional Avatars of 2D RCFT. hep-th/9509151, Nucl. Phys. Proc. Suppl. 46, 130-145 (1996)
7. 5. Nakajima, H.: Heisenberg algebra and Hubert schemes of points on projectivc surfaces alg-geom/9507012; Lectures on Hubert schemes of points on surfaces. H. Nakajima's homepage
8. 6. Losev, A., Moore, G., Nekrasov, N., Shatashvili, S.: Central Extensions of Gauge Groups Revisited. hep-th/9511185
9. 7. Losev, A., Moore, G., Nekrasov, N., Shatashvili, S.: Chiral Lagrangians, Anomalies, Supersymmetry, and Holomorphy. Nucl. Phys. B 484, 196-222 (1997), hep-th/9606082
10. 8. Vafa, C.: Instantons on D-branes. hep-th/9512078, Nucl. Phys. B463, 435-442 (1996)
11. 9. Harvey, J.A., Moore, G.: On the algebras of BPS states. hep-th/9609017
12. 10. Aharony, O., Berkooz, M., Seiberg, N.: Light-cone description of (2, 0) superconformal theories in six dimensions. hep-th/9712117
13. 11. Harvey, J.A. and Strominger, A.: The hetcrotic string is a soliton. hep-th/9504047
14. 12. Sen, A.: String-String Duality Conjecture In Six Dimensions And Charged Solitonic Strings. hep-th/9504027
15. 13. Douglas, M.R.: Enhanced Gauge Symmetry in M(atrix) Theory. hep-th/9612126
16. 14. Donagi, R., Witten, E.: Supersymmetric Yang-Mills Theory and Integrable Systems. hep-th/9510101, Nucl. Phys.B 460, 299-334 (1996)
17. 15. Donagi, R.Y.: Seiberg-Witten integrable systems. alg-geom/9705010
18. 16. Faddeev, L.D.: How algebraic Bethe ansatz works for integrable model. hep-th/9605187
19. 17. Faddeev, L.D.: Algebraic aspects of Bethe ansatz. Int. J. Mod. Phys. A 10,1845-1878 (1995). hep-th/9404013; The Bethe ansatz. SFB-288-70, Jun 1993. Andrejewski lectures
20. 17. Faddeev, L.D.: Algebraic aspects of Bethe ansatz. Int. J. Mod. Phys. A 10,1845-1878 (1995). hep-th/9404013; The Bethe ansatz. SFB-288-70, Jun 1993. Andrejewski lectures
21. 18. Hitchin, N., Karlhede, A., Lindstrom, U. and Rocek, M.: Hyperkähler metrics and supersymmetry. Commun. Math. Phys. 108,535 (1987)
22. 19. Atiyah, M., Bott, R.: The Moment Map And Equivariant Cohomology. Topology 23, 1-28 (1984)
23. 20. Witten, E.: Introduction to Cohomological Field Theories. In: Lectures at Workshop on Topological Methods in Physics, Trieste, Italy, Jun 11-25, 1990, Int. J. Mod. Phys. A6, 2775 (1991)
24. 21. Witten, E.: On Quantum gauge theories in two dimensions. Commun. Math. Phys. 141, 153 (1991)
25. 22. For a review, see S. Cordes, G. Moore, and S. Ramgoolam, Lectures on 2D Yang Mills theory, Equivariant Cohomology, and Topological String Theory. Lectures presented at the 1994 Les Houches Summer School Fluctuating Geometries in Statistical Mechanics and Field Theory, and at the Trieste 1994 Spring school on superstrings. hep-th/9411210, or see http://xxx.lanl.gov/lh94
26. 23. Kirwan, F.: Cohomology of quotients in symplectic and algebraic geometry. Math. Notes, Princeton, NJ: Princeton University Press, 1985
27. 24. Park, J.-S.: Monads and D-instantons. hep-th/9612096
28. 25. Givental, A.B.: Equivariant Gromov-Witten Invariants. alg-geom/9603021
29. 26. Gibbons, G., Rychenkova P.: Hyperkähler quotient construction of BPS Monopole moduli space. hep-th/9608085
30. 27. Kronheimer, P.: The construction of ALE spaces as hyper-kähler quotients. J. Diff. Geom. 28, 665 (1989)
31. 28. Intriligator, K., Seiberg, N.: Mirror Symmetry in Three Dimensional Gauge Theories. hep-th/9607207, Phys. Lett. B 387, 513 (1996)
32. 29. Hitchin, N.: Stable bundles and integrahle systems. Duke Math 54, 91-114 (1987)
33. 30. Hitchin, N.: The self-duality equations on a Riemann surface. Proc. London Math. Soc. 55, 59-126 (1987)
34. 31. Blau, M. and Thompson, G.: Lectures on 2d Gauge Theories: Topological Aspects and Path Integral Techniques. Presented at the Summer School in High Energy Physics and Cosmology. Trieste, Italy, 14 Jun-30 Jul, 1993, hep-th/9310144
35. 32. Blau, M., Thomson, G.: Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model. Nucl. Phys. B 408, 345-390 (1993)
36. 33. Gerasimov, A.: Localization in GWZW and Verlinde formula. hepth/9305090
37. 34. Witten, E.: Supersymmetric Yang-Mills Theory On A Four-Manifold. J. Math. Phys. 35, 5101 (1994)
38. 35. Park, J.-S.: Holomorphic Yang-Mills theory on compact Kähler manifolds. hep-th/9305095; Nucl. Phys. B423, 559 (1994); J.-S. Park: N = 2 Topological Yang-Mills Theory on Compact Kähler Surfaces. Commun. Math, Phys. 163, 113 (1994); S. Hyun and J.-S. Park: N = 2 Topological Yang-Mills Theories and Donaldson Polynomials. hep-th/9404009
39. 35. Park, J.-S.: Holomorphic Yang-Mills theory on compact Kähler manifolds. hep-th/9305095; Nucl. Phys. B423, 559 (1994); J.-S. Park: N = 2 Topological Yang-Mills Theory on Compact Kähler Surfaces. Commun. Math, Phys. 163, 113 (1994); S. Hyun and J.-S. Park: N = 2 Topological Yang-Mills Theories and Donaldson Polynomials. hep-th/9404009
40. 35. Park, J.-S.: Holomorphic Yang-Mills theory on compact Kähler manifolds. hep-th/9305095; Nucl. Phys. B423, 559 (1994); J.-S. Park: N = 2 Topological Yang-Mills Theory on Compact Kähler Surfaces. Commun. Math, Phys. 163, 113 (1994); S. Hyun and J.-S. Park: N = 2 Topological Yang-Mills Theories and Donaldson Polynomials. hep-th/9404009
41. 36. Hyun, S. and Park, J.-S.: Holomorphic Yang-Mills Theory and Variation of the Donaldson Invariants. hep-th/9503036
42. 37. Maciocia, A.: Metrics on the moduli spaces of instantons over Euclidean 4-Space. Commun. Math. Phys. 135, 467 (1991)
43. 38. Kronheimer, P. and Nakajima, H.: Yang-Mills instantons on ALE gravitational instantons. Math. Ann. 288, 263 (1990)