The Sen Limit

TL;DR

This paper introduces a stable version of the Sen limit in F-theory, providing a precise geometric correspondence with perturbative type IIB string theory and linking bulk quantities to boundary expressions.

Contribution

It presents a new stable geometric formulation of the Sen limit, clarifying the F-theory and IIB correspondence through a split into P^1- and conic bundles.

Findings

The elliptic Calabi-Yau splits into two bundles in the stable limit.

A precise match between F-theory and perturbative IIB is established.

Smoothing the Calabi-Yau corresponds to summing D(-1)-instanton corrections.

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.