Vacua of different gaugings of D = 4 N = 8 supergravity that preserve the same supersymmetries and bosonic symmetry tend to exhibit the same universal mass spectrum within their respective supergravities. For AdS 4 vacua in gauged supergravities that arise upon consistent truncation of string/M-theory, we show that this universality is lost at higher Kaluza-Klein levels. However, universality is still maintained in a milder form, as certain sums over a finite number of states remain universal. Further, we derive a mass matrix for Kaluza-Klein gravitons which is valid for all the AdS 4 vacua in string/M-theory that uplift from the gaugings of D = 4 N = 8 supergravity that we consider. The mild universality of mass sums is related to the trace of this mass matrix.

The SU(3)-invariant sector of maximal supergravity in four dimensions with an SO(8) gauging is uplifted to D = 11 supergravity. In order to do this, the SU(3)-neutral sector of the tensor and duality hierarchies of the D = 4 N = 8 supergravity is first worked out. The consistent D = 11 embedding of the full, dynamical SU(3) sector is then expressed at the level of the D = 11 metric and three-form gauge field in terms of these D = 4 tensors. The redundancies introduced by this approach are eliminated at the level of the D = 11 four-form field strength by making use of the D = 4 duality hierarchy. Our results encompass previously known truncations of D = 11 supergravity down to sectors of SO(8) supergravity with symmetry larger than SU(3), and include new ones. In particular, we obtain a new consistent truncation of D = 11 supergravity to minimal D = 4 N = 2 gauged supergravity. The SU(3)-invariant sector of SO(8) supergravityLet us start by reviewing some aspects of the SU(3) sector of SO(8)-gauged supergravity. We choose a triangular, or Iwasawa, parametrisation for the (SU(3)-invariant truncation of the) E 7(7) /SU(8) coset representative. Since previous literature often chooses the unitary gauge for the coset, we believe that our presentation has some intrinsic value even if the material that is covered (the Lagrangian in section 2.1, the further subsectors in 2.3, and the vacuum structure in 2.4) is mostly review. The SU(3)-invariant, restricted tensor and duality hierarchies worked out in section 2.2 are new.

We investigate compactifications of type II and M-theory down to AdS 5 with generic fluxes that preserve eight supercharges, in the framework of Exceptional Generalized Geometry. The geometric data and gauge fields on the internal manifold are encoded in a pair of generalized structures corresponding to the vector and hyper-multiplets of the reduced five-dimensional supergravity. Supersymmetry translates into integrability conditions for these structures, generalizing, in the case of type IIB, the Sasaki-Einstein conditions. We show that the ten and eleven-dimensional type IIB and M-theory Killing-spinor equations specialized to a warped AdS 5 background imply the generalized integrability conditions.

A common way to obtain standard-model-like Lagrangians in string theory is to place D3-branes inside flux compactifications. The bosonic and fermionic masses and couplings of the resulting gauge theory are determined by the ten-dimensional metric and the fluxes, respectively, and the breaking of supersymmetry is soft. However, not any soft-supersymmetry-breaking Lagrangian can be obtained this way since the string theory equations of motion impose certain relations between the soft couplings. We show that for D3-branes in background fluxes, these relations imply that the sums of the squares of the boson and of the fermion masses are equal and that, furthermore, one-and two-loop quantum corrections do not spoil this equality. This makes the use of D3-branes for constructing computationally controllable models for physics beyond the standard model problematic.D-branes provide a very nice mechanism for embedding supersymmetric gauge theories in type II string theory. There is an extensive literature on using branes extended along a (3+1)-dimensional space and wrapping some cycles (or a point) in a six-dimensional (internal) manifold to construct four-dimensional effective theories that have a field content similar to that of the standard model (for reviews, see Refs. [1][2][3]). In these constructions, the low-energy excitations on the branes give the gauge-theory sector, with masses and couplings related to the low-energy closed string modes of the internal manifold.Phenomenologically relevant models arise when nontrivial background fluxes on the internal space are turned on. Whenever these fluxes break supersymmetry in the bulk, this is communicated to the gauge sector through the bulk fields (via, for example, gravitymediation supersymmetry-breaking scenarios), generating soft terms for the matter fields.The main advantage of soft-supersymmetry breaking compared to spontaneous breaking is that the former can avoid the supertrace sum ruleand hence avoid the existence of supersymmetric particles much lighter than the top quark, which is essentially ruled out by recent LHC results. The simplest low-energy theories can be obtained using D3-branes transverse to the six-dimensional manifold -these are U (N ) gauge theories whose field content and symmetries are determined by the geometry of the internal space. To obtain theories that are more relevant phenomenologically, one usually places the D3-branes at singularities in the internal space, which breaks the U (N ) gauge symmetry into standard-model-or grand-unifiedtheory-like gauge groups. As already mentioned, fluxes on the internal manifold induce soft-supersymmetrybreaking terms in the gauge theory [4,5] and one may therefore hope to use these branes to construct realistic models of physics beyond the standard model (BSM).The purpose of this Letter is to show that, even if the breaking of supersymmetry on the D3-branes is soft, the soft terms still obey (1), not only at tree level, but also (at least) at one and two loops. Hence, the treelevel zero-supertrace con...