Gravitational Instantons and Fluxes from M/F-theory on Calabi-Yau fourfolds

TL;DR

This work analyzes circle compactifications of 4d $ ext{N}=1$ gauged supergravity with shift-symmetric scalar fluxes, showing that Taub-NUT instantons provide universal 3d superpotential corrections in the fluxless case, and that fluxes necessitate gauge-instanton completions to preserve invariance. It embeds the construction in M-theory on elliptically fibered Calabi–Yau fourfolds, mapping 3d gaugings to $G_4$ flux data and identifying M5-branes on the base as the instanton source, with anomaly constraints explaining gauge-variant corrections. Nonperturbative corrections of the form $W(T_0) \,=\, \mathcal{A} e^{-2\pi T_0}$ (and flux-augmented variants) yield AdS$_3$ vacua at stabilized radius, and the authors discuss possible uplifts to 4d F-theory vacua and transdimensional tunneling to higher-dimensional vacua. By unifying 4d gauged supergravity, M-theory fluxes, and nonperturbative instantons, the paper advances moduli stabilization and clarifies the structure of AdS vacua in the string/M-theory landscape.

Abstract

We compactify four-dimensional N=1 gauged supergravity theories on a circle including fluxes for shift-symmetric scalars. Four-dimensional Taub-NUT gravitational instantons universally correct the three-dimensional superpotential in the absence of fluxes. In the presence of fluxes these Taub-NUT instanton contributions are no longer gauge-invariant. Invariance can be restored by gauge instantons on top of Taub-NUT instantons. We establish the embedding of this scenario into M-theory. Circle fluxes and gaugings arise from a restricted class of M-theory four-form fluxes on a resolved Calabi-Yau fourfold. The M5-brane on the base of the elliptic fourfold dualizes into the universal Taub-NUT instanton. In the presence of fluxes this M5-brane is anomalous. We argue that anomaly free contributions arise from involved M5-brane geometries dual to gauge-instantons on top of Taub-NUT instantons. Adding a four-dimensional superpotential to the gravitational instanton corrections leads to three-dimensional Anti-de Sitter vacua at stabilized compactification radius. We comment on the possibility to uplift these M-theory vacua, and to tunnel to four-dimensional F-theory vacua.

Figures (2)

• Figure 1: Scalar potential for the radion $r$ before (a) and after (b) the up-lift.
• Figure 2: Brane configuration along the Type IIA compactification circle.