Orientifolds for F-theory on K3 Surfaces

Compactification of F-theory on an elliptically fibered K3 surface provides a framework to encode type IIB string theory on elliptic curves, with the Kaehler modulus of the elliptic curve encoded in the complex structure of the elliptic fibers. In work with Malmendier, Mendez-Diez, and Rosenberg we extend that perspective by examining F-theory orientifolds on elliptically fibered K3 surfaces and connecting them to D-brane classifications using real K-theory (KR-theory). The real structures — antiholomorphic involutions — on our K3 surfaces connect the geometry with the physics, providing a natural setting for understanding the interplay between elliptic fibration structures and D-brane classifications in F-theory. We construct Real normal forms with their associated antiholomorphic involutions and use this to make explicit the 2-torsion Brauer twist that relates our normal forms to the Jacobian (Weierstrass normal form) elliptic fibration, including the realization of a representative for the twisting class as an Azumaya algebra. This all connects back to the physics by considering three families of real K3 surfaces whose string limits give the three different type IIB theories on P1 with four type I_0^∗ Kodaira fibers.

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