Orientifold Limit of F-theory Vacua

Abstract

We show how F-theory on a Calabi-Yau (n+1)-fold, in appropriate limit, can be identified as an orientifold of type IIB string theory compactified on a Calabi-Yau n-fold.

Figures (3)

• Figure 1: In this figure we have displayed a two dimensional sphere $S^2$ embedded in ${\cal M}_n$. The black squares represent points where the D-branes intersect this sphere, and the black circles represent points where the orientifold planes intersect the sphere. The monodromy around a curve enclosing all the squares and the circles must be trivial since this curve can be contracted to a point in $S^2$. This forces the number of circles to be even and the number of squares to be four times the number of circles.
• Figure 2: This figure displays a two dimensional section of ${\cal B}_n$. The black squares represent the zeroes of $(\eta^2+12h\chi)$. The shaded regions denote the region $|h|\sim |C|^{1/2}$, and the two black crosses inside each of the shaded region are the two zeroes of $\Delta$ near $h=0$. A contour around only one of these black crosses must pass through the shaded region, whereas a contour around both crosses can avoid the shaded region. $C_2$ denotes such a contour. $C_1$ is a contour around a zero of $(\eta^2+12h\chi)$. In the unshaded region of this diagram, $Im(\lambda)$ is large. As shown in the text, under F-theory $-$ orientifold correspondence, each shaded region is mapped to a black circle in Fig.1.
• Figure 3: The Duality Cycle