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TMF, 1997, Volume 112, Number 1, Pages 3–46 (Mi tmf1025)  

This article is cited in 21 scientific papers (total in 21 papers)

On integrable systems and supersymmetric gauge theories

A. V. Marshakovab

a P. N. Lebedev Physical Institute, Russian Academy of Sciences
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: The properties of the $\mathcal N=2$ SUSY gauge theories underlying the Seiberg–Witten hypothesis are discussed. The main ingredients of the formulation of the finite-gap solutions to integrable equations in terms of complex curves and generating 1-differential are presented, the invariant sense of these definitions is illustrated. Recently found exact nonperturbative solutions to $\mathcal N=2$ SUSY gauge theories are formulated using the methods of the theory of integrable systems and where it is possible the parallels between standard quantum field theory results and solutions to integrable systems are discussed.

DOI: https://doi.org/10.4213/tmf1025

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English version:
Theoretical and Mathematical Physics, 1997, 112:1, 791–826

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Received: 10.02.1997

Citation: A. V. Marshakov, “On integrable systems and supersymmetric gauge theories”, TMF, 112:1 (1997), 3–46; Theoret. and Math. Phys., 112:1 (1997), 791–826

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D'Hoker, E, “Spectral curves for super-Yang-Mills with adjoint hypermultiplet for general simple Lie algebras”, Nuclear Physics B, 534:3 (1998), 697  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. Gesztesy, F, “Elliptic algebro-geometric solutions of the KdV and AKNS hierarchies - An analytic approach”, Bulletin of the American Mathematical Society, 35:4 (1998), 271  crossref  mathscinet  zmath  isi
    3. Kanno, H, “Picard-Fuchs equation and prepotential of five-dimensional SUSY gauge theory compactified on a circle”, Nuclear Physics B, 530:1–2 (1998), 73  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. D'Hoker, E, “Calogero–Moser Lax pairs with spectral parameter for general Lie algebras”, Nuclear Physics B, 530:3 (1998), 537  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Gorsky, A, “RG equations from Whitham hierarchy”, Nuclear Physics B, 527:3 (1998), 690  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. Marshakov, A, “5d and 6d supersymmetric gauge theories: prepotentials from integrable systems”, Nuclear Physics B, 518:1–2 (1998), 59  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. A. V. Marshakov, “Strings, SUSY gauge theories, and integrable systems”, Theoret. and Math. Phys., 121:2 (1999), 1409–1461  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Takasaki, K, “Whitham deformations and tau functions in N=2 supersymmetric gauge theories”, Progress of Theoretical Physics Supplement, 1999, no. 135, 53  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    9. D'Hoker, E, “Seiberg-Witten theory and Calogero–Moser systems”, Progress of Theoretical Physics Supplement, 1999, no. 135, 75  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    10. Braden, HW, “The Ruijsenaars-Schneider model in the context of Seiberg-Witten theory”, Nuclear Physics B, 558:1–2 (1999), 371  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    11. Krichever, I, “Spin chain models with spectral curves from M theory”, Communications in Mathematical Physics, 213:3 (2000), 539  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    12. Takasaki, K, “Whitham deformations of Seiberg-Witten curves for classical gauge groups”, International Journal of Modern Physics A, 15:23 (2000), 3635  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    13. Mironov A., “WDVV equations and Seiberg-Witten theory”, Integrability: the Seiberg-Witten and Whitham Equations, 2000, 103–123  mathscinet  zmath  isi
    14. D'Hoker E., Phong D.H., “Seiberg-Witten theory and integrable systems”, Integrability: the Seiberg-Witten and Whitham Equations, 2000, 43–68  mathscinet  zmath  isi
    15. A. V. Marshakov, “On Associativity Equations”, Theoret. and Math. Phys., 132:1 (2002), 895–933  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    16. Phys. Usp., 45:9 (2002), 915–954  mathnet  crossref  crossref  isi
    17. D'Hoker E., Phong D.H., “Lectures on supersymmetric Yang-Mills theory and integrable systems”, Theoretical Physics At the End of the Twentieth Century, CRM Series in Mathematical Physics, 2002, 1–125  mathscinet  zmath  adsnasa  isi
    18. Kim S., Lee K.M., Yee H.U., Yi P.J., “The N=1*theories on R1+2 x S-1 with twisted boundary conditions”, Journal of High Energy Physics, 2004, no. 8, 040  crossref  mathscinet  isi
    19. Yang, ZY, “Generalized Toda mechanics associated with loop algebra L(B-r)”, Communications in Theoretical Physics, 43:3 (2005), 407  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    20. Yang, ZY, “Generalized Toda mechanics associated with loop algebras L(C-r) and L(D-r) and their reductions”, Communications in Theoretical Physics, 43:1 (2005), 1  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    21. Braden, HW, “WDVV equations for 6d Seiberg-Witten theory and bi-elliptic curves”, Acta Applicandae Mathematicae, 99:3 (2007), 223  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
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