Supersymmetric scale-separated AdS$_3$ orientifold vacua of type IIB

TL;DR

The paper tackles the problem of achieving supersymmetric $AdS_3$ vacua with a parametric separation of AdS and KK scales in string theory. It introduces a construction in type IIB string theory on seven-manifolds with co-closed $G_2$-structures, realized via $ obreak ext{Z}_2^3$ orbifolds of twisted tori and nilmanifolds with smeared O5-planes; fluxes are arranged so that some remain unbounded and drive a controlled regime with weak coupling and large volumes, enabling scale separation in the nilmanifold sector. The solvmanifold sector yields SUSY $AdS_3$ vacua but does not conclusively exhibit AdS-to-KK scale separation within the analyzed flux constraint. A notable finding is that some spectra, particularly on $ obreakrak{n}_2$, have integer conformal dimensions in the putative holographic dual. The results suggest that supersymmetric, scale-separated $AdS_3$ vacua in type IIB with classical ingredients are possible and invite further holographic and geometric investigations.

Abstract

I construct supersymmetric AdS$_3$ vacua of type IIB string theory that exhibit parametric scale separation in the controlled regime. These solutions arise from compactifications on seven-dimensional manifolds equipped with co-closed $G_2$-structures, in the presence of orientifold planes preserving minimal supersymmetry. I focus on $\mathbb{Z}_2^3$ orbifolds of a specific solvmanifold and all seven-dimensional nilmanifolds, each requiring distinct configurations of intersecting O5-planes, which are treated in the smeared approximation. Weak string coupling and large volumes can be achieved for classical backgrounds on both nilmanifolds and solvmanifolds by tuning unbounded fluxes to large values. This achieves scale separation in the nilmanifold case, but the same cannot be concluded for the solvmanifolds. Furthermore, for some solutions, the holographic field theory operators dual to the lightest scalar fields have integer conformal dimensions at tree level, as in other scale-separated type IIA orientifold backgrounds.

Figures (5)

• Figure 1: Masses squared for nilmanifold $\mathfrak{n}_4$ for 16 different values of $\rho$, left and right for a scalar with negative and positive mass squared, respectively.
• Figure 2: Masses squared for nilmanifold $\mathfrak{n}_6$ dependent on $\tau$, for the $-$ branch (left) and $+$ branch (right). For all lines, $a=1$, except for the red and purple, which are normalised with $a=8$ and $a=48$ respectively.
• Figure 3: Masses squared for nilmanifold 37B$_1$ dependent on $\tau$, for the $-$ branch (left) and $+$ branch (right). For all lines, $a=1$, except for the brown one, which is normalised with $a=4$. The plot of the $-$ branch starts from $\tau =1$, as the solution is only consistent for this branch when $\tau>1$.
• Figure 4: Masses squared for nilmanifold 37C dependent on $\tau$, for the $-$ branch (left) and $+$ branch (right). For all lines, $a=1$, except for the red and purple, which are normalised with $a=8$ and $a=48$ respectively.
• Figure 5: Masses squared dependent on $\tau$, for the $-$ branch (left) and $+$ branch (right). For all lines, $a=1$, except for the upper curve in light blue, which is normalised with $a=4$. The green curve (third highest up) has multiplicity 2. For the $-$ branch, $\rho$ is only positive if $\tau > \sqrt{3}$ and hence the plot starts from this value.