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Izv. RAN. Ser. Mat., 1999, Volume 63, Issue 1, Pages 107–122 (Mi izv230)  

This article is cited in 1 scientific paper (total in 1 paper)

$S$-duality testing and exceptional bundles

B. V. Karpov


Abstract: In this paper we discuss algebraic-geometric problems connected with the mathematical testing of the $S$-duality conjecture. In particular, we give a complete description of the field configurations in classical gauge theories for which the coefficient of the Gell–Mann–Low beta-function in the one-loop approximation equals zero. Realizing one of these configurations geometrically on Del Pezzo surfaces, we demonstrate its relation to exceptional bundles: every exceptional bundle whose cohomology is zero and whose slope is negative but exceeds the slope of the canonical class gives a correlation function for $S$-duality testing.

DOI: https://doi.org/10.4213/im230

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English version:
Izvestiya: Mathematics, 1999, 63:1, 103–117

Bibliographic databases:

MSC: 53C07, 81T30
Received: 02.10.1997

Citation: B. V. Karpov, “$S$-duality testing and exceptional bundles”, Izv. RAN. Ser. Mat., 63:1 (1999), 107–122; Izv. Math., 63:1 (1999), 103–117

Citation in format AMSBIB
\Bibitem{Kar99}
\by B.~V.~Karpov
\paper $S$-duality testing and exceptional bundles
\jour Izv. RAN. Ser. Mat.
\yr 1999
\vol 63
\issue 1
\pages 107--122
\mathnet{http://mi.mathnet.ru/izv230}
\crossref{https://doi.org/10.4213/im230}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1701840}
\zmath{https://zbmath.org/?q=an:0974.81041}
\transl
\jour Izv. Math.
\yr 1999
\vol 63
\issue 1
\pages 103--117
\crossref{https://doi.org/10.1070/im1999v063n01ABEH000230}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746946469}


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  • https://doi.org/10.4213/im230
  • http://mi.mathnet.ru/eng/izv/v63/i1/p107

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Tyurin, “Instantons and monopoles”, Russian Math. Surveys, 57:2 (2002), 305–360  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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