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\(F\)-theory and orientifolds. (English) Zbl 0925.81181

Summary: By analyzing \(F\)-theory on \(K3\) near the orbifold limit of \(K3\) we establish the equivalence between \(F\)-theory on \(K3\) and an orientifold of type IIB on \(T^{2}\), which in turn is related by a \(T\)-duality transformation to type I theory on \(T^{2}\). By analyzing the \(F\)-theory background away from the orbifold limit, we show that nonperturbative effects in the orientifold theory split an orientifold plane into two planes, with nontrivial SL\((2,\mathbb{Z})\) monodromy around each of them. The mathematical description of this phenomenon is identical to the Seiberg-Witten result for \(N=2\) supersymmetric SU(2) gauge theory with four quark flavors. Points of enhanced gauge symmetry in the orientifold/\(F\)-theory are in one-to-one correspondence with the points of enhanced global symmetry in the Seiberg-Witten theory.

MSC:

81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32J81 Applications of compact analytic spaces to the sciences
83E30 String and superstring theories in gravitational theory
81T60 Supersymmetric field theories in quantum mechanics
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