SOLUTIONS OF MATTER-COUPLED HALF-MAXIMAL GAUGED SUPERGRAVITY IN FOUR AND FIVE DIMENSIONS
In this thesis, we present holographic and de-Sitter (dS) solutions of matter-coupled half- maximal gauged supergravity (SUGRA) in four and five dimensions using the embedding tensor formalism. In the first part, we study the 5D N = 4 gauged supergravity coupled to five vector multiplets with compact gauge group U(1) × SU(2) × SU(2), as well as non-compact gauge groups U(1) × SO(3,1) and U(1) × SL(3,R). In the second part, we switch our focus from holographic solutions to the cosmologically relevant dS solutions in N = 4 gauged 5D and 4D SUGRAs. Using the embedding tensor formalism, our dS solutions were derived by requiring the vanishing of certain fermionic shift matrices encoding the gauging parameters of the theory, while keeping the scalar potential extremized at a positive value. This procedure leads to a systematic classification of all possible dS vacua with semisimple gaugings. Moreover, within the embedding tensor formalism, our method can be applied to supergravity theories in any other dimensions with any number of supercharges.
Supergravity, de-Sitter, Noncompact gaugings, AdS-CFT, Holography
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