F-theory and Orientifolds

TL;DR

This paper explores the relationship between F-theory on K3 surfaces and type IIB orientifolds, revealing non-perturbative effects that split orientifold planes and connect to Seiberg-Witten theory.

Contribution

It establishes a detailed correspondence between F-theory on K3, orientifold theories, and Seiberg-Witten results, including non-perturbative phenomena.

Findings

F-theory on K3 is equivalent to type IIB orientifold on T^2.

Non-perturbative effects split orientifold planes with SL(2,Z) monodromy.

Enhanced gauge symmetries correspond to Seiberg-Witten points.

Abstract

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 non-perturbative effects in the orientifold theory splits an orientifold plane into two planes, with non-trivial SL(2,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.