Scale-separated AdS$_2$ flux vacua from type II

Abstract

Motivated by the question of whether the internal scales of a compactification can be parametrically decoupled from the external curvature scale, and by the possibility of probing such vacua holographically, we construct the first AdS$_2$ flux vacua with parametric scale separation. We compactify type II string theory on a $G_2$ structure orbifold times a circle in the presence of smeared spacetime-filling O1/O5-planes or O4/O8-planes, together with NSNS and RR fluxes. We derive the two-dimensional dilaton-gravity effective theory and exhibit families of vacua in which unbounded $F_5$ and $H_7$ fluxes provide parametric control in type IIB, while unbounded $F_4$, $F_8$, and $H_7$ fluxes provide parametric control in type IIA. For large flux quanta, the string coupling becomes parametrically weak, all internal bulk radii become parametrically large in string units, and the Kaluza--Klein scale separates from the $\mathrm{AdS}_2$ curvature scale. We analyze the ten-dimensional Killing-spinor equations and identify parametric branches preserving $\mathcal N=(1,1)$ supersymmetry in two dimensions. We explain how our geometrically scale-separated AdS$_2$ vacua are compatible with a recent no-go theorem for scale separation in theories with extended supersymmetry. Finally, we discuss various T-dualities leading to other type IIB and type IIA compactifications on $G_2$ structure spaces times a circle and $SU(3)$ structure spaces times a two-torus.