The Sen Limit

Abstract

F-theory compactifications on elliptic Calabi-Yau manifolds may be related to IIb compactifications by taking a certain limit in complex structure moduli space, introduced by A. Sen. The limit has been characterized on the basis of SL(2,Z) monodromies of the elliptic fibration. Instead, we introduce a stable version of the Sen limit. In this picture the elliptic Calabi-Yau splits into two pieces, a P^1-bundle and a conic bundle, and the intersection yields the IIb space-time. We get a precise match between F-theory and perturbative type IIb. The correspondence is holographic, in the sense that physical quantities seemingly spread in the bulk of the F-theory Calabi-Yau may be rewritten as expressions on the log boundary. Smoothing the F-theory Calabi-Yau corresponds to summing up the D(-1)-instanton corrections to the IIb theory.

Figures (1)

• Figure 1: Picture of elliptic fibers for $g_s=0$, before and after blow-up. (a) The generic fiber consists of a line and a conic. They intersect in two points, with monodromy around $b_2=0$. This intersection is identified with the IIb space-time. Contracting the conic leaves a nodal curve. (b) At the $D7$ locus $b_2 b_6 - b_4^2=0$, the conic degenerates to a pair of lines. Blowing down the degenerate conic yields again a nodal curve. (c) At the $O7$ locus $b_2 = 0$ the line and the conic are tangent. Upon blowing down the conic, we get a cusp.