Global properties of the conformal manifold for S-fold backgrounds
Alfredo Giambrone, Emanuel Malek, Henning Samtleben, Mario Trigiante
Abstract
A bstract We study a one-parameter family of $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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)] ⋉ ℝ 12 . These backgrounds are known to correspond to Type IIB S-fold solutions with internal manifold of topology S 1 × S 5 . The family of AdS 4 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 $$ \frac{2\pi }{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> <mml:mi>T</mml:mi> </mml:mfrac> </mml:math> , 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 χ . At the special values χ = 0 and χ = $$ \frac{\pi }{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mi>π</mml:mi> <mml:mi>T</mml:mi> </mml:mfrac> </mml:math> , the symmetry enhances according to U(1) 2 → U(2), giving rise however to inequivalent Kaluza-Klein spectra. At χ = $$ \frac{\pi }{T} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mi>π</mml:mi> <mml:mi>T</mml:mi> </mml:mfrac> </mml:math> , 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.