Machine Learning Gauged Supergravity

Abstract

Type IIB string theory on a 5-sphere gives rise to  = 8, SO(6) gauged supergravity in five dimensions. Motivated by the fact that this is the context of the most widely studied example of the AdS/CFT correspondence, we undertake an investigation of its critical points. The scalar manifold is an E 6(6) ∕USp(8) coset, and the challenge is that it is 42-dimensional. We take a Machine Learning approach to the problem using TensorFlow, and this results in a substantial increase in the number of known critical points. Our list of 32 critical points contains all five of the previously known ones, including an  = 2 supersymmetric point identified by Khavaev, Pilch and Warner.

Brane-jet stability of non-supersymmetric AdS vacua

“…This follows from [7,8], where the extrema of that gauged supergravity were scanned: all the non-supersymmetric extrema have Kaluza-Klein (KK) excitations, contained within the N = 8 supergravity, with mass below the Breitenlohner-Freedman (BF) bound [9]. Similar classification results exist [10,11] for AdS 4 × S 7 vacua of M-theory that uplift [12] from extrema of D = 4 N = 8 SO(8)-gauged supergravity [13].…”

“…Further comments on the symmetries of the critical points in table 1 will be made in appendix B. We emphasise that the present classification is not exhaustive within the full N = 8 theory: a complete classification along the lines of [7,8,11] should still be made.…”

“…It is noticeable that, while the SO (8) gauging [13] of D = 4 N = 8 supergravity has only one critical point [14] which is non-supersymmetric and BF-stable within its N = 8 theory [11,16], the dyonic ISO (7) gauging [11,25] has at least the seven ones contained in the seven-chiral subsector. A comprehensive scan of critical points within the full D = 4 N = 8 ISO(7) theory along the lines of [7,8,11] would be timely and very interesting, but it is beyond the scope of this paper. The upshot of this analysis of BF-stable vacua within D = 4 N = 8 ISO(7) supergravity is summarised in table 1.…”

“…The upshot of this analysis of BF-stable vacua within D = 4 N = 8 ISO(7) supergravity is summarised in table 1. The residual N < 8 supersymmetry, bosonic symmetry group G ⊂ SO (7) and the cosmological constant (in units involving c ≡ m/g, with g > 0 the electric and m > 0 the magnetic couplings of the N = 8 supergravity) are recorded. The groups SU(3) and G 2 therein are the unique such subgroups of SO(7), while SO(3) d and SO(3) R are embedded into SO(7) as in (B.1).…”

“…withvol7 given in(3.12).WZ terms for the D8-brane. The termĈ 3 ∧B 2 3 contributes to (3.20) aŝC 3 ∧B 2 3 = −6 ∆ 3v ol 9 , (C.11)…”