Scale-Separated Vacua with Extended Supersymmetry

• Scale-separated vacua with extended supersymmetry are AdS backgrounds where the curvature scale is much larger than the UV cutoff, enabling decoupling of heavy modes.
• Quantum gravity constraints like flux quantization and the weak gravity conjecture restrict scale separation, especially in higher-dimensional supergravity theories.
• Recent explicit constructions in massive IIA using circle compactifications demonstrate that appropriate fluxes and O6/D6 configurations can achieve genuine scale separation in AdS₃ vacua.

Scale-separated vacua with extended supersymmetry refer to anti-de Sitter (AdS) or related backgrounds in which the curvature (AdS) scale $L_{\mathrm{AdS}}$ is parametrically larger than the ultraviolet cutoff of the effective theory, such as the Kaluza–Klein (KK) scale or the tension of the lightest BPS object. These vacua exhibit extended supersymmetry—$\mathcal{N} \geq 2$ in $d=3,4,5$—which imposes rigid constraints on moduli stabilization, flux quantization, and the structure of allowed compactifications. The question of whether genuine scale separation is compatible with extended supersymmetry has formed a central theme in string theory and quantum gravity research, particularly in the context of "swampland" constraints.

1. Definition and Motivation for Scale Separation

Scale separation is defined by a hierarchy between the AdS curvature radius $L_{\mathrm{AdS}}$ and the UV cutoff scale $\Lambda_\mathrm{UV}$, typically set by the lowest KK or stringy excitation: $\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$ or equivalently, in terms of the ratio of the KK to AdS scales,

$$\epsilon \equiv \frac{L_{\mathrm{AdS}}}{L_{\mathrm{KK}}} \gg 1$$

Achieving such a hierarchy is crucial for the self-consistency of a lower-dimensional effective supergravity: lighter new states should not appear at or below the AdS scale, so that physics below $\Lambda_\mathrm{UV}$ decouples from heavy and stringy modes. Scale separation is also necessary for the validity of the AdS/CFT correspondence in a regime where the gravitational description is trustworthy and the dual CFT has a large gap.

The pursuit of scale-separated AdS compactifications with extended supersymmetry addresses both foundational quantum-gravity consistency questions and practical issues in moduli stabilization, holography, and phenomenology (Cribiori et al., 2022, Cribiori et al., 2023, Cribiori et al., 2024, Cribiori et al., 29 Apr 2026).

2. Quantum Gravity Constraints: No-go Theorems for Extended Supersymmetry

A common theme in recent research is the existence of universal constraints forbidding scale separation in AdS vacua with extended supersymmetry. In $d=4,5$ supergravity, the weak gravity conjecture (WGC) (Cribiori et al., 2022), the species scale (Cribiori et al., 2023), and flux quantization arguments collectively enforce that the AdS scale is not parametrically larger than the KK or species cutoff: $L_{\mathrm{AdS}} \lesssim L_{\mathrm{KK}}$ In $\mathcal{N} \geq 2$0—the context relevant for AdS$\mathcal{N} \geq 2$1 flux vacua—(Cribiori et al., 2024) proves that the AdS radius $\mathcal{N} \geq 2$2 is always of the same order, or smaller, than the tension $\mathcal{N} \geq 2$3 of a fundamental BPS domain-wall 0-brane, which itself bounds the UV cutoff: $\mathcal{N} \geq 2$4 This arises because supersymmetric flux compactifications necessarily preserve BPS domain walls whose charge/tension quantization is tied to the flux quantum, precluding any parametric separation. The absence of scale separation therefore appears as a corollary of extended SUSY, BPS completeness, and quantum gravity consistency.

Proven cases include:

• AdS$\mathcal{N} \geq 2$5 with $\mathcal{N} \geq 2$6 supersymmetry: the AdS cosmological constant is set by charges and gauged coupling, which is upper-bounded by the WGC (Cribiori et al., 2022).
• AdS$\mathcal{N} \geq 2$7 with $\mathcal{N} \geq 2$8 (and intermediate cases): the cosmological constant is entirely fixed by R-symmetry gauging; WGC and species arguments again eliminate the possibility of $\mathcal{N} \geq 2$9 (Cribiori et al., 2023).
• AdS$d=3,4,5$0 with $d=3,4,5$1: flux vacua must have BPS domain walls whose tension sets the cutoff, enforcing $d=3,4,5$2 (Cribiori et al., 2024).

This collection of results motivated conjectures that scale separation may generically be incompatible with extended SUSY in controlled string vacua.

3. Explicit Constructions: Scale-Separated Vacua in Massive IIA

Recent work (Cribiori et al., 29 Apr 2026) provides explicit constructions of scale-separated AdS$d=3,4,5$3 vacua with extended $d=3,4,5$4 supersymmetry, evading previously established no-go arguments. These models are built as circle compactifications of four-dimensional massive type IIA vacua (notably DGKT and CFI orbifolds) by threading new fluxes and arranging mutually supersymmetric O6-planes and D6-branes.

The compactification manifold is: $d=3,4,5$5 with $d=3,4,5$6 (DGKT) or $d=3,4,5$7 (CFI), and includes both bulk fluxes (Romans mass $d=3,4,5$8, $d=3,4,5$9, $L_{\mathrm{AdS}}$0) and localized sources (four O6-planes, three stacks of D6-branes).

The critical feature is that, by an appropriate choice of fluxes $L_{\mathrm{AdS}}$1 and balancing tadpole conditions $L_{\mathrm{AdS}}$2, all geometric moduli are stabilized and the AdS$L_{\mathrm{AdS}}$3 radius can be made parametrically larger than the KK scale: $L_{\mathrm{AdS}}$4 with $L_{\mathrm{AdS}}$5 the magnitude of the flux quantum. The resulting vacua possess extended (four real) supercharges in $L_{\mathrm{AdS}}$6, corresponding to $L_{\mathrm{AdS}}$7.

This construction circumvents previous barriers by leveraging the product structure and additional fluxes of the compactification, as well as the specific intersection configuration of O6/D6 sources that leaves $L_{\mathrm{AdS}}$8 SUSY intact (Cribiori et al., 29 Apr 2026).

4. Effective Theory and Moduli Stabilization

Reduction to $L_{\mathrm{AdS}}$9 yields an $\Lambda_\mathrm{UV}$0 supergravity with closed-string moduli:

• The chiral multiplets are $\Lambda_\mathrm{UV}$1 (dilaton-volume), $\Lambda_\mathrm{UV}$2 (complexified sizes of two-tori), and $\Lambda_\mathrm{UV}$3 (circle-radius multiplet).
• The Kähler potential and superpotential are

$\Lambda_\mathrm{UV}$4

$\Lambda_\mathrm{UV}$5

with $\Lambda_\mathrm{UV}$6 encoding couplings from the new fluxes.

Supersymmetric AdS$\Lambda_\mathrm{UV}$7 vacua solve $\Lambda_\mathrm{UV}$8, fully stabilizing all untwisted moduli. The scalar mass spectrum derived from the Hessian is non-tachyonic (one mode saturates the Breitenlohner–Freedman bound), and conformal dimensions of dual operators are non-integer, demonstrating that $\Lambda_\mathrm{UV}$9 supersymmetry in three dimensions does not enforce integrality of spectrum (Cribiori et al., 29 Apr 2026).

5. Physical Implications and Relations to Swampland Criteria

The existence of explicit, controlled scale-separated AdS$\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$0 vacua with extended supersymmetry expands the landscape of string solutions and challenges prior "swampland" expectations. Key implications include:

• Extended supersymmetry can co-exist with scale separation, at least in three dimensions, if additional fluxes and source configurations are allowed.
• Non-integer conformal dimensions are compatible with scale separation and $\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$1 SUSY in AdS$\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$2.
• The models offer a well-controlled setting to study holography, protected by additional supercharges, and to test "emergent string" and WGC-related conjectures in lower dimensions.

A summary table contrasts the vacua explored in this context:

Dimension & Supersymmetry	Scale-separated vacua	Key obstruction or mechanism
$\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$3	$\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$4	No
$\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$6	$\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$7	Yes
$\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$8	$\Lambda_\mathrm{UV} L_{\mathrm{AdS}} \gg 1$9	No
$$\epsilon \equiv \frac{L_{\mathrm{AdS}}}{L_{\mathrm{KK}}} \gg 1$$0	$$\epsilon \equiv \frac{L_{\mathrm{AdS}}}{L_{\mathrm{KK}}} \gg 1$$1	Yes

This suggests that the dimensionality and details of the compactification, fluxes, and localized sources can decisively influence the realization of scale separation in the presence of extended supersymmetry.

6. Open Questions and Generalizations

Several directions remain under active investigation:

• Generalization to AdS$$\epsilon \equiv \frac{L_{\mathrm{AdS}}}{L_{\mathrm{KK}}} \gg 1$$2 or AdS$$\epsilon \equiv \frac{L_{\mathrm{AdS}}}{L_{\mathrm{KK}}} \gg 1$$3 with genuine scale separation and extended supersymmetry remains unachieved, with current no-go arguments still standing (Cribiori et al., 2022, Cribiori et al., 2023).
• Classification of all allowed source and flux arrangements compatible with scale separation and extended SUSY is open, especially in light of accidental enhancements in lower dimensions.
• The status of non-supersymmetric or $$\epsilon \equiv \frac{L_{\mathrm{AdS}}}{L_{\mathrm{KK}}} \gg 1$$4 vacua that evade WGC-based obstructions, and their quantum stability, remains debated.
• Exploration of the dual CFTs with non-integer conformal dimensions in these vacua, and the implications for holography and modular invariance.

The constructions in (Cribiori et al., 29 Apr 2026) thus establish the existence of fully stabilized, weakly coupled, scale-separated AdS$$\epsilon \equiv \frac{L_{\mathrm{AdS}}}{L_{\mathrm{KK}}} \gg 1$$5 vacua with extended supersymmetry, opening a new arena for testing the limits of quantum gravity constraints and effective field theory in string compactifications.