Global Properties of the Conformal Manifold for S-Fold Backgrounds

TL;DR

This paper explores a family of AdS vacua in supergravity linked to Type IIB S-fold solutions, revealing the true periodic nature of a modulus and its impact on the spectrum and symmetry of the solutions.

Contribution

The authors provide the 10-dimensional geometric interpretation of the modulus and explicitly compute the Kaluza-Klein spectrum as a function of this modulus.

Findings

The modulus has a periodicity of 2π/T, matching the inverse radius of S^1.

Symmetry enhances at specific modulus values, leading to inequivalent spectra.

Additional massless vectors appear at special points, exemplifying the 'space invaders' scenario.

Abstract

We study a one-parameter family of $\mathcal{N}=2$ anti-de Sitter vacua with ${\rm U}(1)^2$ symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group $[{\rm SO}(6)\times {\rm SO}(1,1)]\ltimes \mathbb{R}^{12}$. These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology $S^1\times S^5$. The family of AdS$_4$ vacua is parametrized by a modulus $\chi$. Although $\chi$ appears non-compact in the four-dimensional supergravity, we show that this is just an artefact of the four-dimensional description. We give the 10-dimensional geometric interpretation of the modulus and show that it actually has periodicity of $\frac{2\pi}{T}$, which is the inverse radius of $S^1$. We deduce this by providing the explicit $D=10$ uplift of the family of vacua as well as computing the entire modulus-dependent Kaluza-Klein spectrum as a function of $\chi$. At the special values $\chi=0$ and $\chi=\frac{\pi}{T}$, the symmetry enhances according to ${\rm U}(1)^2\rightarrow{\rm U}(2)$, giving rise however to inequivalent Kaluza-Klein spectra. At $\chi=\frac{\pi}{T}$, this realizes a bosonic version of the "space invaders" scenario with additional massless vector fields arising from formerly massive fields at higher Kaluza-Klein levels.