Compactification-specific uplift source data in a 4D moduli EFT

Fix a local field patch and the four-dimensional Einstein-frame normalization of a compactification-derived two-derivative moduli EFT. A compactification-specific uplift source datum is a tuple consisting of a declared source sector and its contribution $\mathrm{\Delta }{V}_{\mathrm{s}\mathrm{r}\mathrm{c}}(Z,\bar{Z})=Df(Z,\bar{Z})$ to the scalar potential on that patch. Here $Z=(Z^I)$ is the stated list of retained complex scalar coordinates, $D$ is a real coefficient with units of energy density, and $f$ is a real dimensionless profile in the same coordinates. The tuple records the coefficient normalization and its frame conversion; whether the source is localized or smeared; the warp factor used; worldvolume fields and charges; the induced or shifted tadpole data; and the backreaction and correction terms retained, omitted, or separately bounded.

The profile and coefficient depend on the source action, geometry, warp convention, modulus coordinate, and Weyl normalization. This definition assigns no universal power of the total volume and does not identify a nilpotent-superfield parameterization with a localized string source. It is an EFT input record, not a derivation of that input.

Kachru, Kallosh, Linde, and Trivedi, §III.B

McAllister and Quevedo, §4.3

McAllister, Moritz, Nally, and Schachner, §3.3

Compactification-derived four-dimensional moduli EFT data