Supersymmetric objects in gauged supergravities

This thesis is focused on supersymmetric objects in gauged supergravities and their interpretation in string theory. Three particular theories are considered and analyzed: matter-coupled $d=4, 5$ abelian gauged supergravities with 8 supercharges and minimal $d=7$ gauged supergravity with 16 supercharges. Respectively in the $d=4$ and $d=5$ cases, the BPS first-order flows of static extremal black holes and black strings are studied using the Hamilton-Jacobi formalism. The attractor mechanism is formulated for the case of couplings to hypermultiplets and two exact BPS black hole solutions are derived in $d=4$ from the first-order equations obtained with the Hamilton-Jacobi approach. One of these black holes manifests an $\mathrm{AdS}_4$ asymptotics which has not yet a clear explanation in string theory. Within the minimal $d=7$ theory, a class of asymptotically $\mathrm{AdS}_7$ BPS solutions involving a non-trivial profile for a 3-form gauge potential is derived and analyzed in relation to the embedding in M-theory and massive IIA string theory. The holographic interpretation of a particular asymptotically $\mathrm{AdS}_7$ solution characterized by an $\mathrm{AdS}_3$ slicing of the 7-dimensional background is formulated in terms of a conformal defect $\mathcal{N}=(4,0)$ $\mathrm{SCFT}_2$ within the $\mathcal{N}=(1,0)$ $\mathrm{SCFT}_6$ dual to the $\mathrm{AdS}_7$.