Systematics of the $\alpha'$ Expansion in F-Theory

TL;DR

This paper develops a systematic understanding of perturbative string corrections in F-theory compactifications, revealing that only even powers of ' corrections contribute at any order, with odd powers arising from KK and winding mode effects.

Contribution

It introduces a dual approach using rescaling symmetries and F/M-theory duality to determine the moduli dependence and ' order of corrections in F-theory compactifications.

Findings

Only ' even corrections are generated at any order in M-theory reductions.

' odd effects originate from integrating out KK and winding modes.

Leading no-scale breaking effects occur at '^3 order, with possible logarithmic corrections.

Abstract

Extracting reliable low-energy information from string compactifications notoriously requires a detailed understanding of the UV sensitivity of the corresponding effective field theories. Despite past efforts in computing perturbative string corrections to the tree-level action, neither a systematic approach nor a unified framework has emerged yet. We make progress in this direction, focusing on the moduli dependence of perturbative corrections to the 4D scalar potential of type IIB Calabi-Yau orientifold compactifications. We proceed by employing two strategies. First, we use two rescaling symmetries of type IIB string theory to infer the dependence of any perturbative correction on both the dilaton and the Calabi-Yau volume. Second, we use F/M-theory duality to conclude that KK reductions on elliptically-fibred Calabi-Yau fourfolds of the M-theory action at any order in the derivative expansion can only generate $(\alpha')^{\rm even}$ corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that $(\alpha')^{\rm odd}$ effects arise from integrating out KK and winding modes on the elliptic fibration and argue that the leading no-scale breaking effects at string tree-level arise from $(\alpha')^3$ effects, modulo potential logarithmic corrections.