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We illustrate the recent construction of gauged extended supergravity models in four dimensions featuring webs of anti-de Sitter vacua, preserving different amounts of supersymmetries or no supersymmetry at all, connected by flat directions of the scalar potential.
One class of vacua was found in maximal gauged supergravity and effectively describes S-fold backgrounds of Type IIB superstring theory. Some of the flat directions are interpreted in terms global geometric properties of the internal compact manifold.The second class of vacua was found in a gauged N=3 model with gauge group SO(3) x SU(3). As opposed to the first class of solutions, their uplift to string/M-theory backgrounds is still an open problem.We briefly touch upon the possible interpretation of the flat directions in terms of exactly marginal deformations of the dual (super-) conformal field theory.