Gauged supergravities and the physics of extra dimensions

PhD ceremony: Mr. G. Dibitetto, 11.00 uur, Academiegebouw, Broerstraat 5, Groningen

Dissertation: Gauged supergravities and the physics of extra dimensions

Promotor(s): prof. E.A. Bergshoeff

Faculty: Mathematics and Natural Sciences

This thesis analyses supergravities in various dimensions and their possible origin from compactifications of string theory.

The lower-dimensional theories arising from flux compactifications are the so-called gauged supergravities. Before the gauging procedure the theory is invariant under a certain global symmetry group which is interpreted as string duality. In gauged supergravities a certain subgroup of the global symmetry is made local and the structure constants of the gauge algebra appear in the theory as deformation parameters generating a potential for the scalarfields of the theory. The gauging breaks the invariance under the duality symmetry and still the theory can be made duality covariant by promoting the deformation parameters to tensors (embedding tensor) with respect to the global symmetry.

The first important point of this thesis is that physics after compactification is only sensitive to the orbits of the global symmetry group, in that gaugings lying in the same group orbit are related by duality transformations. Given a certain gauged supergravity containing non-geometric fluxes, it becomes a natural question whether there exists a duality transformation that rotates them away. Thus the classification of duality orbits becomes relevant in order to answer this question. In this thesis we give this classification for maximal and half-maximal supergravities in dimension seven and higher. In the maximal case we find that every orbit admits a geometric representative.

Conversely, there appear non-geometric orbits in the half-maximal case. This implies that geometric flux compactifications are insuficient for describing all the lower-dimensional effective theories. In these cases we give an interpretation as compactifications of Double Field Theory (DFT). Focusing then on our better understanding of geometric flux compactifications, we analyse further in this thesis a class of compactifications down to four dimensions which are compatible with half-maximal supersymmetry (orientifold compactifications). Firstly we give the full dictionary between (non-)geometric uxes and embedding tensor components of N = 4 gauged supergravity. Secondly, we restrict to those theories admitting only geometric uxes in type II string theories. The complete set of vacua is found: in type IIB only known Minkowski solutions with at directions appear, whereas in type IIA there are both known and novel AdS solutions. The unexpected feature of the above AdS solutions in type IIA is their compatibility with the total absence of supersymmetry-breaking sources. This implies that these solutions can be uplifted to N = 8 supergravity. Thus we analyse how these type IIA solutions are embedded in maximal supergravity. After computing the full mass spectrum of the scalars, we find the remarkable presence of non-supersymmetric and nevertheless stable critical points.