F-theory and orientifolds

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, Z) monodromy around each of them. The mathematical description of this phenomenon is identified Ito 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.