Systematics of the ${\alpha }^{\prime }$ Expansion in F-Theory

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 $({\alpha }^{\prime }{)}^{\mathrm{even}}$ corrections to the 4D scalar potential, which, moreover, all vanish for trivial fibrations. We finally give evidence that $({\alpha }^{\prime }{)}^{\mathrm{odd}}$ 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 $({\alpha }^{\prime }{)}^3$ effects, modulo potential logarithmic corrections.

36 pages plus appendices, 4 figures

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