Type IIB supergravity compactified on a Calabi-Yau manifold with H-fluxes

TL;DR

This work analyzes Type IIB supergravity compactified on a Calabi–Yau manifold with both NS and RR $H$-fluxes. By deriving the four-dimensional scalar potential through direct compactification and through ${\cal N}=2$ gauged supergravity, the authors show the two approaches yield the same result after the appropriate Einstein-frame rescaling, resolving previous discrepancies. The resulting potential is positive semidefinite and exhibits run-away behavior in hypermultiplet directions, with no finite critical points in the classical regime unless the volume is driven to infinity; a consistent ${\cal N}=1$ vacuum would require a nontrivial truncation (e.g., freezing hypermultiplets). The analysis clarifies the role of the full quaternionic structure and the necessity of including all contributions (including the $E$-term) to obtain a correct gauged-supergravity form, while highlighting limits on achieving ${\cal N}=1$ vacua in this setup.

Abstract

We discuss the compactification of type IIB supergravity on a Calabi-Yau manifold in the presence of both RR and NS fluxes for the three-form fields. We obtain the classical potential both by direct compactification and by using the techniques of N=2 gauged supergravity in four-dimensions. We briefly discuss the properties of such potential and compare the result with previous derivations.