Non-supersymmetric heterotic strings on $AdS_{4}\times S^{3}\times S^{3}$

TL;DR

This paper studies the stability of non-supersymmetric heterotic string compactifications on AdS4 times two 3-spheres, revealing complex instability phenomena including tachyons and brane nucleation.

Contribution

It provides a detailed analysis of flux-induced stability and instability mechanisms in a novel non-supersymmetric heterotic string background.

Findings

Tachyonic modes appear when fluxes are close, but can be projected out by orbifolding.

Large separation of fluxes results in inverse scale separation without tachyons.

Non-perturbative brane nucleation always offers decay channels, influencing flux dynamics.

Abstract

We analyze the stability properties of a family of anti-de Sitter flux compactifications of the tachyon-free non-supersymmetric heterotic string in ten dimensions. In contrast with simpler such solutions, the solutions include two independent unbounded fluxes, leading to richer instability phenomena. In particular, when the two fluxes are sufficiently close in magnitude, the perturbative spectrum develops tachyonic modes, which can be projected out by an orbifold action. When the fluxes are far apart, tachyonic modes are absent, and the geometry displays inverse scale separation, where a factor of the internal manifold becomes parametrically larger than the anti-de Sitter factor. Still, non-perturbative instabilities in the form of brane nucleation are always available decay channels, and tend to drive the two fluxes closer together, eventually triggering the tachyonic instability when present.