Generalized Flux Vacua

TL;DR

The work analyzes generalized flux compactifications of Type II string theory on a symmetric $T^6/\mathbb{Z}_2$ orientifold, incorporating geometric and nongeometric NS-NS/R-R fluxes within a duality-invariant framework. It derives a polynomial superpotential $W = P_1(\tau) + S P_2(\tau) + 3U P_3(\tau)$ and solves the ${\cal N}=1$ F-flat conditions to stabilize all moduli, obtaining parametric control over the string coupling $g=1/{\rm Im}\,S$ and the cosmological constant $\Lambda = -3 e^{K}|W|^2$ in many vacua. The paper reveals two infinite families of nongeometric vacua saturating the RR tadpole without D-branes and demonstrates, via numerical statistics, an apparently infinite number of SUSY vacua within finite regions of parameter space, while also discussing caveats about lifting these to full string backgrounds and the role of $\,\alpha'\$ effects. These findings point to a rich, possibly new class of nongeometric string vacua and raise important questions about the finiteness of the landscape and the criteria for UV completion.

Abstract

We consider type II string theory compactified on a symmetric T^6/Z_2 orientifold. We study a general class of discrete deformations of the resulting four-dimensional supergravity theory, including gaugings arising from geometric and "nongeometric'' fluxes, as well as the usual R-R and NS-NS fluxes. Solving the equations of motion associated with the resulting N = 1 superpotential, we find parametrically controllable infinite families of supersymmetric vacua with all moduli stabilized. We also describe some aspects of the distribution of generic solutions to the SUSY equations of motion for this model, and note in particular the existence of an apparently infinite number of solutions in a finite range of the parameter space of the four-dimensional effective theory.