Abstract^*

In this project we would like to work on various aspects of three dimensional gauged supergravity (gSUGRA) theories. Our motivation has its roots in the seminal work of Maldacena [1], which put forward a brilliant idea relating two completely different theories and conjectured the equivalence between string theory on an Anti de Sitter (AdS) space and a conformal field theory (CFT) defined on the boundary of the AdS space. The “AdS/CFT conjecture” also provides a very powerful calculational tool, because one can determine physically important quantities on the theory with strong-coupling using perturbative methods on the weakly-coupled side. It has passed various checks in different dimensions and been verified several times by considering different limiting cases. This conjecture is arguably one of the most remarkable ideas ever put forward by string theory, and has found a wide range of applications including e.g. condensed matter theory. The low energy limit of string theory on an AdS background is generally a gSUGRA, and among those, the three dimensional ones are especially important, since a lot has already been known on two dimensional CFTs [2] that, according to this conjecture, would live on the boundary of a three dimensional spacetime. Moreover, three dimensional gravity theories provide good toy models for testing various ideas in quantum gravity since they share several of the physically important properties of the four dimensional gravitational models, including specifically Einstein’s General Relativity, but lack thereof many of the complications inherent in their counterparts [3]. The general method for the construction of D=3 gSUGRA theories with different amounts of supersymmetry (SUSY) is given in [4]. Unfortunately, very few explicit D=3 gSUGRA models are known to date [5]. Hence we would like to work on, among other things, the construction of D=3 gSUGRA models in this project. 

Our first goal is to explicitly construct the D=3, N=4 gSUGRA models with different manifolds for the scalar fields and with different gaugings, i.e. with different ways of breaking the R-symmetry to give charge to the gravitinos. To do this, we will use the techniques discussed in [4]. Once we construct some explicit models, we will study various properties that they may have. These include, but are not limited to, finding exact solutions, working out their physical properties, identifying their higher dimensional origins, and studying the relevant renormalization group (RG) flows. Specifically, it would be quite interesting to find out the model that comes from the consistent S² reduction of the D=5, N=1 minimal SUGRA theory. The action of this theory does not include a typical Maxwell or Yang-Mills type, but has a generalized, topological Chern-Simons type term for the vector fields. A consistent S²reduction for such a theory has never been done before, so this would be quite a novel result.

Our second goal is to find explicitly new supersymmetric solutions of matter coupled D=3, N=8 gSUGRA theories [6] with nonvanishing vector fields. The six and ten dimensional origins of this theory are well known. Previously in [7], we initiated a systematic study of the supersymmetric solutions of these theories by employing a Killing spinor analysis and found some exact solutions for their ungauged versions. We now want to extend this earlier analysis by considering nonvanishing vector fields. We expect that the black string and black hole geometries will belong to this class of solutions. Once these solutions are obtained, one can also work out their properties, and especially find out their higher dimensional origins, which would be an important result since such an uplifting has not been done before.

As a third goal, we would like to extend our earlier results [8,9] on the D=3, N=2 gSUGRA model constructed in [10] by applying the afore-mentioned Killing spinor analysis to find and classify all supersymmetric solutions of this theory. Moreover, we also want to generalize the RG flow analysis carried out in [11] for this model with an active vector field, using the charged black string solutions found in [8,9]. Another open problem for the model in [10] is to find its string/M-theory origin so that its CFT dual can be identified. We also want to address these open problems in this project.

We expect that the open problems we have briefly mentioned above will take about three years of research. In this project, we may collaborate with Prof. Dr. Henning Samtleben (ENS de Lyon, France) and Ast. Prof. Dr. Dieter Van den Bleeken (Boğaziçi Univ.). We also gladly have the opportunity to discuss possible technical issues with Prof. Dr. Ergin Sezgin (Texas A&M, ABD) and Prof. Dr. Ali Kaya (Boğaziçi Üniv.) as well.

^*: Please refer to the part “4. Literatür Özeti” for the details of the references indicated by numbers within brackets in the text.