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

TL;DR

This paper explores how gravitational instantons and fluxes in M/F-theory compactifications on Calabi-Yau fourfolds influence superpotentials, gauge invariance, and vacuum structures, revealing new instanton contributions and potential AdS vacua.

Contribution

It establishes the embedding of Taub-NUT and gauge instantons into M-theory on Calabi-Yau fourfolds, detailing flux effects and anomaly cancellations, and discusses implications for three-dimensional AdS vacua.

Findings

Taub-NUT instantons correct the superpotential without fluxes.

Fluxes break gauge invariance of instanton contributions, which can be restored by gauge instantons.

Adding superpotentials leads to stabilized AdS vacua in three dimensions.

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.