A landscape of non-supersymmetric AdS vacua on coset manifolds

TL;DR

This work constructs new non-supersymmetric, sourceless AdS$_4$ vacua in type IIA on coset manifolds with SU(3)-structure by preserving the underlying geometry while varying NSNS/RR fluxes within a structured expansion. Using an Englert-type ansatz and a detailed left-invariant flux expansion, the authors derive a set of algebraic conditions for flux coefficients and obtain explicit non-SUSY solutions on cosets such as $rac{ ext{Sp(2)}}{ ext{S}( ext{U(2)} imes ext{U(1)})}$ and $rac{ ext{SU(3)}}{ ext{U(1)} imes ext{U(1)}}$, including rich families parametrized by shape variables like $oldsymbol{\sigma}$. A stability analysis against left-invariant fluctuations reveals that many of these vacua are BF-stable within this sector, though some Englert-type branches are unstable depending on the coset and region in parameter space. The results suggest a sizable non-supersymmetric AdS$_4$ landscape with potential CFT duals, while flux quantization and non-left-invariant modes remain important avenues for future work and for exploring potential de Sitter constructions within no-go safe regions.

Abstract

We construct new families of non-supersymmetric sourceless type IIA AdS4 vacua on those coset manifolds that also admit supersymmetric solutions. We investigate the spectrum of left-invariant modes and find that most, but not all, of the vacua are stable under these fluctuations. Generically, there are also no massless moduli.

Figures (4)

• Figure 1: $\frac{\text{Sp(2)}}{\text{S}(\text{U(2)}\times \text{U(1)})}$-model: plot of $a R_{\text{4D}}$ for the supersymmetric solutions (light green) and the new non-supersymmetric solutions (other colors) in terms of the shape parameter $\sigma$. Unstable solutions are indicated in red.
• Figure 2: Plots of the solutions on the coset $\frac{\text{Sp(2)}}{\text{S}(\text{U(2)}\times \text{U(1)})}$. Different colors indicate different solutions. Unstable solutions are indicated in red (see section \ref{['stab']}) and the supersymmetric solutions in light green. By a suitable rescaling of the coefficients the dependence on the overall scale $a$ is taken out.
• Figure 3: Spectrum of left-invariant modes of the solutions on $\frac{\text{Sp(2)}}{\text{S}(\text{U(2)}\times \text{U(1)})}$ and $\frac{\text{SU(3)}}{\text{U(1)}\times \text{U(1)}}$.
• Figure 4: $\frac{\text{SU(3)}}{\text{U(1)}\times \text{U(1)}}$-model: plot of $a R_{\text{4D}}$ in terms of the shape parameter $\sigma$. Unstable solutions are indicated in red.