We study a one-parameter family of $$ \mathcal{N} $$ 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 $$ \frac{2\pi }{T} $$ 2 π 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 = $$ \frac{\pi }{T} $$ π T , the symmetry enhances according to U(1)2 → U(2), giving rise however to inequivalent Kaluza-Klein spectra. At χ = $$ \frac{\pi }{T} $$ π 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.
Considering matter coupled supersymmetric Chern-Simons theories in three dimensions we extend the Gaiotto-Witten mechanism of supersymmetry enhancement N 3 = 3 → N 3 = 4 from the case where the hypermultiplets span a flat HyperKähler manifold to that where they live on a curved one. We derive the precise conditions of this enhancement in terms of generalized Gaiotto-Witten identities to be satisfied by the tri-holomorphic moment maps. An infinite class of HyperKähler metrics compatible with the enhancement condition is provided by the Calabi metrics on T ⋆ P n . In this list we find, for n = 2 the resolution of the metric cone on N 0,1,0 which is the unique homogeneous Sasaki Einstein 7-manifold leading to an N 4 = 3 compactification of M-theory. This leads to challenging perspectives for the discovery of new relations between the enhancement mechanism in D = 3, the geometry of M2-brane solutions and also for the dual description of super Chern Simons theories on curved HyperKähler manifolds in terms of gauged fixed supergroup Chern Simons theories. The relevant supergroup is in this case SU(3|N) where SU(3) is the flavor group and U(N) is the color group.
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