A cornucopia of AdS5 vacua

A bstract We report on a systematic search for AdS 5 vacua corresponding to critical points of the potential in the five-dimensional N N = 8 SO (6) gauged supergravity. By employing Google’s TensorFlow Machine Learning library, we find the total of 32 critical points including 5 previously known ones. All 27 new critical points are non-supersymmetric. We compute the mass spectra of scalar fluctuatons for all points and find that the non- supersymmetric AdS 5 vacua are perturbatively unstable. Many of the new critical points can be found analytically within consistent truncations of the N N = 8 supergravity with respect to discrete subgroups of the S (O (6) × GL (2, ℝ) ) symmetry of the potential. In par- ticular, we discuss in detail a Z₂³ ℤ 2 3 -invariant truncation with 10 scalar fields and 15 critical points. We also compute explicitly the scalar potential in a Z₂² ℤ 2 2 -invariant extension of that truncation to 18 scalar fields and reproduce 17 of the 32 critical points from the numerical search. Finally, we show that the full potential as a function of 42 scalar fields can be studied analytically using the so-called solvable parametrization. In particular, we find that all critical points lie in a ℤ 2 -invariant subspace spanned by 22 scalar fields.