Geodesic
$S$-duality testing and exceptional bundles
Izvestiya. Mathematics , Tome 63 (1999) no. 1, pp. 103-117

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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. 
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     title = {$S$-duality testing and exceptional bundles},
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B. V. Karpov. $S$-duality testing and exceptional bundles. Izvestiya. Mathematics , Tome 63 (1999) no. 1, pp. 103-117. http://geodesic.mathdoc.fr/item/IM2_1999_63_1_a4/