Warped Compactifications in M and F Theory

TL;DR

This work analyzes warped compactifications in M- and F-theory on Calabi–Yau four-folds with background G-flux, deriving an explicit warp factor in orbifold limits and exploring its impact on the 4D effective theory. The warp factor is sourced purely by backreaction and is computed using Green's functions, separating constant and localized flux contributions; topological constraints determine the massless spectrum despite warping. In the explicit K3×K3 example, two moduli are lifted by G-flux, leaving 38 N=2 vector multiplets, while the leading relation between 4D and higher-dimensional Planck scales remains intact, indicating gravity is not localized as in RS scenarios. Overall, the paper demonstrates that flux backreaction can be incorporated consistently in warped M/F-theory vacua and that moduli counting can still be guided by topology, laying groundwork for more general CY4 analyses and brane-world phenomenology.

Abstract

We study M and F theory compactifications on Calabi-Yau four-folds in the presence of non-trivial background flux. The geometry is warped and belongs to the class of p-brane metrics. We solve for the explicit warp factor in the orbifold limit of these compactifications, compare our results to some of the more familiar recently studied warped scenarios, and discuss the effects on the low-energy theory. As the warp factor is generated solely by backreaction, we may use topological arguments to determine the massless spectrum. We perform the computation for the case where the four-fold equals K3 \times K3.