We derive conditions for the existence of four-dimensional $\mathcal{N}=1$ supersymmetric flux vacua of massive type IIA string theory with general supergravity fluxes turned on. For an SU(3) singlet Killing spinor, we show that such flux vacua exist when the internal geometry is nearly Kähler. The geometry is not warped, all the allowed fluxes are proportional to the mass parameter, and the dilaton is fixed by a ratio of (quantized) fluxes. The four-dimensional cosmological constant, while negative, becomes small in the vacuum with the weak string coupling.

• Received 5 March 2004

DOI:https://doi.org/10.1103/PhysRevLett.95.021601