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# Advances in Theoretical and Mathematical Physics

## Volume 18 (2014)

### Number 3

### The Sen limit

Pages: 613 – 658

DOI: http://dx.doi.org/10.4310/ATMP.2014.v18.n3.a2

#### Authors

#### 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 $SL(2, \mathrm{Z})$ 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 $\mathbf{P}^1$-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.