Title:

Holographic renormalisation group flows and supergravity

This thesis can be divided into two related parts. In the first part the idea of the holographic beta function is reviewed and a new method is developed that allows to compute the scalar potential of onescalar truncations of the fivedimensional gauged supergravity theory, provided that the beta function of the field theory is classical. A class of deformations that is likely to have a classical beta function are the N = 1 preserving operators in short multiplets of the N = 4. We classify all singletrace operators with such properties, and give extra emphasis to Fterms and Dterms. By writing the deformations in the most general way in terms of N = 1 superfields we find interesting relations to pairs of KaluzaKlein towers that originate from the same tendimensional field in the gravity dual. The ideas of the holographic beta function can be generalized to vacuum expectation values, we record some basic observations, and give an outlook for future work. In the second part a full uplift of the GPPZ flow to ten dimensions is constructed using the exceptional field theory formalism. We obtain the metric, the axiondilaton matrix, and a full set of RR potentials and fluxes, which are checked to satisfy the IIB equations of motion. The uplift contains an extended version of the GPPZ solution where the mass term m and the gaugino condensate are complex, and a U(1) gauge field Aμ is included for consistency. We argue that the phases of the complex scalars are related to the U(1)R and the bonus U(1) symmetries of the field theory. We complete a thorough analysis of the asymptotics of the uplift close to the conformal boundary and close to the singularity. While the nearboundary asymptotics are found to agree with the zerotemperature limit of the FreedmanMinahan analysis, we could not fully match with the PolchinskiStrassler solution. The nearsingularity limits confirm and extend the results of PilchWarner. We show that there are conformal frames in which the singularity in the Ricci scalar is improved, but never completely eliminated. In order to relate the singularity to the presence of Dbranesa search for Dbrane sources is initiated and the first preliminary results are positive. In anticipation of a future KaluzaKlein analysis of the solution we start a systematic derivation of corresponding spherical harmonic functions.
