O(16)$\times$O(16) heterotic theory on $AdS_3\times S^3\times T^4$

TL;DR

This work analyzes non-supersymmetric $O(16)\times O(16)$ heterotic string theory on $AdS_{3}\times S^{3}\times T^{4}$ with flux quanta, focusing on tree-level vacua, the impact of one-loop corrections, and perturbative stability. The tree-level potential fixes the radii and dilaton in terms of fluxes, yielding a negative cosmological constant $\Lambda_{3}$; incorporating the genus-one correction introduces a positive contribution but cannot uplift to de Sitter for any flux configuration. A detailed fluctuation analysis in the six-dimensional effective theory shows all scalar and tensor modes relevant to the $AdS_3\times S^3$ sector remain above the Breitenlohner-Freedman bound, while the torus moduli can approach the BF bound depending on the Narain moduli and flux parameter $s=\lambda n_5^2/|n_1|$. Scaling arguments indicate higher-order corrections are suppressed for large $|n_5|$, keeping the regime under perturbative control, though intrinsically quantum vacua may become unstable beyond a finite $s$ in some cases. Overall, the paper demonstrates perturbatively stable AdS vacua in a non-supersymmetric heterotic setup without a viable de Sitter uplift, and outlines avenues for further exploration of moduli spaces and worldsheet perspectives.

Abstract

In this paper, we study non-supersymmetric $O(16)\times O(16)$ heterotic theory on an $AdS_{3}\times S^{3}\times T^{4}$ background, finding a family of vacua parameterized by a pair of flux integers. Adding the one-loop scalar potential to the effective theory contributes positively to the cosmological constant, but we find that there is no uplift to de Sitter for any values of the fluxes. We study the fluctuations around these vacua and show that all scalar and tensor modes from the six-dimensional effective theory lie above the Breitenlohner-Freedman bound. The moduli coming from the torus compactification will also be above the bound, at least for a large range of fluxes.

Figures (1)

• Figure 1: Plots of $L_{o}, g_{o}$ and $V_{\text{min}}$ against $\log n_{1}$ for different values of $n_{5}$ given in the legend.