Abstract
This paper deals with algebro-geometric questions arising in the verification of theS-duality conjecture for supersymmetric Yang-Mills quantum field theories in the four-dimensional case. We describe all the cases for the gauge groups of rank 1 and 2, where the Gell-Man-Law beta-function is either zero or negative, and point out some series of such cases for gauge groups of arbitrary rank. Realization of one of these series on the complex projective plane demonstrates a relationship with exceptional bundles.
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References
C. Montonen and D. Olive, “Magnetic monopoles as gauge particle”,Phys. Lett. 72B, 117–132 (1977).
G. Vafa and E. Witten, “A strong coupling test ofS-duality”Nuclear Phys. B,431, 3–77 (1995).
Ph. C. Argyres, M. R. Plesser, and N. Seiberg, “The moduli space of Vacua ofN=2 SUSY QCD and duality inN=2 SUSY QCD”,Nuclear Phys. B,471, 159–194 (1996).
R. Donagi and E. Witten, “Supersymmetric Yang-Mills theory and integrable systems”,Nuclear Phys. B,460, 299–334 (1996).
W. Fulton and J. Harris,Representation Theory. 1st Course, Springer-Verlag, Berlin (1990).
A. L. Gorodentsev and M. I. Leenson,How to calculate the correlation function in twisted SYM N=2, N f=4 QFT on projective plane, Preprint No. 96-49, Max-Planck-Institut für Mathematik, Bonn (1996).
S. A. Kuleshov,Moduli Space of Bundles on a Quadric, Preprint No. 242 18, Warwick (1996).
E. Witten, “Monopoles and four-manifolds”,Math. Res. Letts.,1, 769–796 (1994).
V. Pidstrigach and A. N. Tyurin, “Invariants of smooth structure of an algebraic surface given by the Dirac operator”,Izv. Akad. Nauk SSSR Ser. Mat. Math. USSR-Izv.,52, No. 2, 279–371 (1992).
S. Donaldson and P. Kronheimer,The Geometry of Four-Manifolds, Clarendon Press, Oxford (1990).
W.-M. R. Leung,On Spinℂ-Invariants of Four-Manifolds, Ph. D. Thesis, Magdalen College, Oxford (1995).
A. A. Klyachko, “Moduli of vector bundles and numbers of classes”,Funktsional. Anal. i Prilozhen. [Functional Anal Appl.],25, No. 1, 81–83 (1991).
N. A. Tyurin, “Necessary and sufficient condition for deformation of aB-monopole into an instanton”Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],60, No. 1, 211–224 (1996).
S. A. Kuleshov and D. O. Orlov, “Exceptional sheaves on del Pezzo surfaces”,Izv. Akad. Nauk SSSR Ser. Mat. [Math. USSR-Izv.],58, No. 3, 53–87 (1994).
A. L. Gorodentsev and A. N. Rudakov, “Exceptional vector bundles on projective spaces”,Duke Math. J.,54, 115–130 (1987).
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Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 163–178, February, 1997.
Translated by S. K. Lando
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Karpov, B.V. On the algebraic geometry ofS-duality. Math Notes 61, 133–145 (1997). https://doi.org/10.1007/BF02355724
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DOI: https://doi.org/10.1007/BF02355724