M-theory and Type IIA Flux Compactifications

TL;DR

The authors address the obstruction to flux compactifications in 11D supergravity by identifying new brane-charge sources from higher-derivative couplings, notably an M5-brane tadpole encoded in a covariant $C_6\wedge X_5$ term (duality of the familiar $C_3\wedge X_8$). They develop a duality-based framework to generate these couplings, derive their brane-worldvolume realizations, and construct explicit Minkowski and AdS$_4$ flux vacua in M-theory and Type IIA, including ${\cal N}=1$ and ${\cal N}=2$ examples, with explicit torus-fibration and orientifold structures. The work clarifies how flux, geometry (geometric flux), and higher-derivative couplings can evade the Gibbons no-go and produce smooth flux backgrounds, while it also analyzes the viability of massive IIA flux vacua and finds significant obstacles to achieving large volume or weak coupling limits within that framework. Overall, the paper maps a duality-driven route from M-theory/F-theory constructions to IIA/M-theory flux vacua, highlighting the central role of $C_6\wedge X_5$-type couplings and geometric flux in stabilizing moduli and generating consistent tadpoles. The results offer a concrete path toward smooth, higher-dimensional flux vacua, while delineating current limitations and open questions in the massive IIA regime.

Abstract

We consider compactifications of M-theory and type IIA string theory to four dimensions. For Minkowski space-time, a supergravity no-go theorem forbids flux supported in the internal space. We show how to evade this no-go theorem by exhibiting new sources of brane charge: in string theory, the basic physical phenomenon is the generation of new brane charges from D-branes in transverse fluxes. In M-theory, there is a new source of M5-brane charge from novel higher derivative couplings that involve fluxes as well as curvatures. We present some explicit orientifold examples with both N=1 and N=2 space-time supersymmetry. Finally, we explain the status of massive type IIA flux compactifications.