Geodesic
On the algebraic geometry of $S$-duality
Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 163-178.

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This paper deals with algebro-geometric questions arising in the verification of the $S$-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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B. V. Karpov. On the algebraic geometry of $S$-duality. Matematičeskie zametki, Tome 61 (1997) no. 2, pp. 163-178. http://geodesic.mathdoc.fr/item/MZM_1997_61_2_a0/

[1] Montonen C., Olive D., “Magnetic monopoles as gauge particle”, Phys. Lett. B, 72 (1977), 117–132 | DOI

[2] Vafa G., Witten E., “A strong coupling test of $S$-duality”, Nuclear Phys. B, 431 (1995), 3–77 | DOI | MR

[3] Argyres Ph. C., Plesser M. R., Seiberg N., “The moduli space of Vacua of $N=2$ SUSY QCD and duality in $N=2$ SUSY QCD”, Nuclear Phys. B, 471 (1996), 159–194 | DOI | MR | Zbl

[4] Donagi R., Witten E., “Supersymmetric Yang–Mills theory and integrable systems”, Nuclear Phys. B, 460 (1996), 299–334 | DOI | MR | Zbl

[5] Fulton W., Harris J., Representation Theory, 1st Course, Springer-Verlag, Berlin, 1990

[6] Gorodentsev A. L., Leenson M. I., 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, Bohn, 1996

[7] Kuleshov S. A., Moduli Space of Bundles on a Quadric, Preprint No. 18, Warwick, 1996

[8] Witten E., “Monopoles and four-manifolds”, Math. Res. Letts., 1 (1994), 769–796 | MR | Zbl

[9] Pidstrigach V., Tyurin A. N., “Invarianty gladkoi struktury algebraicheskoi poverkhnosti, zadavaemye operatorom Diraka”, Izv. RAN. Ser. matem., 52:2 (1992), 279–371 | MR

[10] Donaldson S., Kronheimer P., The Geometry of Four-Manifolds, Clarendon Press, Oxford, 1990 | Zbl

[11] Leung W.-M. R., On $\textrm{Spin}^{\mathbb C}$-Invariants of Four-Manifolds, Thesis Ph. D., Magdalen College, Oxford, 1995

[12] Klyachko A. A., “Moduli vektornykh rassloenii i chisla klassov”, Funktsion. analiz i ego prilozh., 25:1 (1991), 81–83 | MR | Zbl

[13] Tyurin N. A., “Neobkhodimoe i dostatochnoe uslovie deformatsii $B$-monopolya v instanton”, Izv. RAN. Ser. matem., 60:1 (1996), 211–224 | MR | Zbl

[14] Kuleshov S. A., Orlov D. O., “Isklyuchitelnye puchki na poverkhnostyakh del Petstso”, Izv. RAN. Ser. matem., 58:3 (1994), 53–87 | MR | Zbl

[15] Gorodentsev A. L., Rudakov A. N., “Exceptional vector bundles on projective spaces”, Duke Math. J., 54 (1987), 115–130 | DOI | MR | Zbl