Schmidt, Stanislav
(2018)
Holographic renormalisation group flows and supergravity.
*University of Southampton, Doctoral Thesis*, 276pp.

## Abstract

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 one-scalar truncations of the five-dimensional 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 single-trace operators with such properties, and give extra emphasis to F-terms and D-terms. By writing the deformations in the most general way in terms of N = 1 superfields we find interesting relations to pairs of Kaluza-Klein towers that originate from the same ten-dimensional 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 axion-dilaton 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 near-boundary asymptotics are found to agree with the zero-temperature limit of the Freedman-Minahan analysis, we could not fully match with the Polchinski-Strassler solution. The near-singularity limits confirm and extend the results of Pilch-Warner. 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 D-branesa search for D-brane sources is initiated and the first preliminary results are positive. In anticipation of a future Kaluza-Klein analysis of the solution we start a systematic derivation of corresponding spherical harmonic functions.

**Final thesis - Version of Record**

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