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Holographic renormalisation group flows and supergravity

Holographic renormalisation group flows and supergravity
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 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.
University of Southampton
Schmidt, Stanislav
5dc0de39-708e-4de5-b124-ba36a4c6eb6f
Schmidt, Stanislav
5dc0de39-708e-4de5-b124-ba36a4c6eb6f
Evans, Nicholas
33dfbb52-64dd-4c1f-9cd1-074faf2be4b3
Skenderis, Konstantinos
09f32871-ffb1-4f4a-83bc-df05f4d17a09

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

Record type: Thesis (Doctoral)

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.

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Published date: May 2018

Identifiers

Local EPrints ID: 423471
URI: http://eprints.soton.ac.uk/id/eprint/423471
PURE UUID: 08e3d34b-7c9f-40d2-9c82-7ee10254d792
ORCID for Konstantinos Skenderis: ORCID iD orcid.org/0000-0003-4509-5472

Catalogue record

Date deposited: 24 Sep 2018 16:30
Last modified: 14 Mar 2019 01:36

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Contributors

Author: Stanislav Schmidt
Thesis advisor: Nicholas Evans
Thesis advisor: Konstantinos Skenderis ORCID iD

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