A note on smeared branes in flux vacua and gauged supergravity

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.

23 pages, LaTeX, no figures; added reference for section 2

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• 7-dimensional $\mathcal{N}=2$ Consistent Truncations using $\mathrm{SL}(5)$ Exceptional Field Theory
• New supersymmetric vacua on solvmanifolds
• A new 6d fixed point from holography
• BPS domain walls from backreacted orientifolds
• Noncompact gauging of N=2 7D supergravity and AdS/CFT holography
• New N=5,6, 3D gauged supergravities and holography
• Flux Backgrounds and Exceptional Generalised Geometry
• On SUSY-breaking Moduli Spaces of AdS${}_7$ Vacua and 6D SCFTs