Global properties of the conformal manifold for S-fold backgrounds

We study a one-parameter family of N = 2 anti-de Sitter vacua with U(1)(2) symmetry of gauged four-dimensional maximal supergravity, with dyonic gauge group [SO(6) x SO(1, 1)] (sic) R-12 These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology S-1 x 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 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 = pi/T, the symmetry enhances according to U(1)(2) -> U(2), giving rise however to in- equivalent Kaluza-Klein spectra. At chi = 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.

Automated summary

We study a one-parameter family of N = 2 anti-de Sitter vacua with U(1)^2 symmetry, corresponding to Type IIB S-fold solutions with internal manifold of topology S^1 x S^5. The modulus has a periodicity of 2π/T in the 10-dimensional geometric interpretation. Enhancements in symmetry occur at specific values of chi, leading to inequivalent Kaluza-Klein spectra.