A note on smeared branes in flux vacua and gauged supergravity

TL;DR

This note shows that, in massive IIA compactifications yielding $AdS_7$ with D6-branes and $H$-flux, localization preserves supersymmetry while smearing breaks it, yet neither case admits a seven-dimensional gauged supergravity description when analyzed through the embedding tensor formalism. The authors map ten-dimensional flux data to 7D embedding-tensor deformations in both half-maximal and maximal theories and demonstrate a no-go condition $h f_0=0$ for consistency, implying no brane-inclusive $AdS_7$ ground state within these 7D gaugings. They argue that the observed breakdown is tied to the absence of scale separation between the $AdS_7$ radius and the KK scale, and conjecture that true lower-dimensional vacua with such separation would admit a gauged supergravity description and resist the SUSY-breaking effects of smearing. The work highlights fundamental limits of smeared reductions in highly supersymmetric flux vacua and motivates a deeper examination of warped effective theories in the presence of extended sources.

Abstract

In the known examples of flux vacua with calibrated spacetime-filling sources (branes or orientifold planes), one can smear the source in order to perform a standard KK reduction and obtain a lower-dimensional supergravity description. Furthermore, it is expected that the smeared and localized solution preserve equal amounts of supersymmetry. In this note we point out that the $\mathrm{AdS}_7$ solution discussed in arXiv:1111.2605 and arXiv:1309.2949 is a counterexample to this common lore. The solution is supersymmetric when the spacetime-filling D6-branes are localized but breaks supersymmetry in the smeared limit. By using the embedding tensor formalism we demonstrate that there is no gauged supergravity description for the solution, regardless of the source being smeared or not. We conjecture that for flux solutions with separation between the KK scale and the AdS radius this cannot occur.