Perturbative stability of intrinsically quantum vacua at T4 critical points

Determine whether any critical points in the T4 Narain moduli space of the non-supersymmetric O(16)×O(16) heterotic string compactified on AdS3×S3×T4 admit perturbatively stable intrinsically quantum vacua in the limit of vanishing electric H3 flux (n1=0), or whether all such vacua become unstable due to one or more torus-modulus fields acquiring masses below the Breitenlohner–Freedman bound.

Background

The paper analyzes O(16)×O(16) heterotic string theory on AdS3×S3×T4 with two H3 flux integers (n1 on AdS3 and n5 on S3), incorporating one-loop corrections to the effective potential. Tree-level vacua are AdS and cannot be uplifted to de Sitter by the one-loop potential. Scalar and tensor modes from the six-dimensional effective theory lie above the BF bound for a broad range of fluxes.

In the large-s regime (effectively n1→0), the authors identify intrinsically quantum vacua whose existence is controlled by the one-loop potential. Preliminary evidence suggests potential instabilities in torus moduli for some flux choices, motivating a detailed paper at specific critical points (e.g., those associated with rank-4 even lattices in the Narain moduli space).

The open problem targets the existence (or non-existence) of perturbatively stable intrinsically quantum vacua at such critical points when the electric flux is turned off, focusing on whether any modulus falls below the BF bound.

References

In particular, we will address the open problem of whether any of these critical points can host perturbatively stable examples of the intrinsically quantum vacua (where the electric flux n1 is set to zero), or whether they all develop instabilities in this limit due to some modulus field dropping below the Breitnlohner-Freedman bound.

— O(16)$\times$O(16) heterotic theory on $AdS_3\times S^3\times T^4$ (2510.20915 - Robbins et al., 23 Oct 2025) in Discussion and outlook