Global properties of the conformal manifold for S-fold backgrounds

Abstract

We study a one-parameter family of $\mathcal{N}$ = 2 anti-de Sitter vacua with U(1)² symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group [SO(6) × SO(1, 1)] ⋉ ℝ¹². These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology S¹ × S⁵. The family of AdS₄ vacua is parametrized by a modulus χ. Although χ 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 S¹. 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 χ. At the special values χ = 0 and χ = $\frac{\pi }{T}$, the symmetry enhances according to U(1)² → U(2), giving rise however to inequivalent Kaluza-Klein spectra. At χ = $\frac{\pi }{T}$, 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.