AdS4 flux vacua in type II superstrings and their domain-wall solutions

TL;DR

The work develops a coherent framework for supersymmetric AdS$_4$ vacua in perturbative type II string theory by combining flux compactifications with gauged supergravity, showing how all moduli can be stabilized in IIA (without geometric flux) and in certain IIB non-geometric setups. It then furnishes a detailed source-brane picture where AdS$_4$ arises as the near-horizon geometry of domain-wall brane distributions, with careful treatment of Bianchi identities and tadpole cancellation, including smeared sources. The authors provide explicit examples, including a fully stabilized D4/D8/NS5 configuration and its IIB mirror, connecting the 4d effective superpotential analysis to ten-dimensional supergravity near-horizon limits. The work highlights the role of smeared sources in enabling perturbative stabilization, discusses the mirror map between IIA and IIB fluxes, and offers a bridge to microscopic entropy considerations via dual brane systems, while noting limitations and avenues for future study in non-geometric realms and holography.

Abstract

We investigate the emergence of supersymmetric negative-vacuum-energy ground states in four dimensions. First, we rely on the analysis of the effective superpotential, which depends on the background fluxes of the internal manifold, or equivalently has its origin in the underlying gauged supergravity. Four-dimensional, supersymmetric anti-de Sitter vacua with all moduli stabilized appear when appropriate Ramond and Neveu--Schwarz fluxes are introduced in IIA. Geometric fluxes are not necessary. Then the whole setup is analyzed from the perspective of the sources, namely D/NS-branes or Kaluza--Klein monopoles. Orientifold planes are also required for tadpole cancellation. The solutions found in four dimensions correspond to domain walls interpolating between AdS4 and flat spacetime. The various consistency conditions (equations of motion, Bianchi identities and tadpole cancellation conditions) are always satisfied, albeit with source terms. We also speculate on the possibility of assigning (formal) entropies to AdS4 flux vacua via the corresponding dual brane systems.