Holographic RG flows and boundary conditions in a 3D gauged supergravity

In this work we focus on the study of RG flows of conformal field theories that are holographically dual to Poincar\'e domain wall solutions in $D=3$, $\mathcal{N}=(2,0)$ gauged supergravity coupled to a sigma model with target space $SU(1, 1)/U(1) = H^2$. This theory is truncated to a subsector where the vector field and phase of the scalar field vanish and we consider different boundary conditions for the remaining real scalar field. The RG flows, which are mostly non-superysymmetric, are analyzed by treating the supergravity field equations as a dynamical system for the scalar field and its derivative with respect to the scale factor. Phase diagrams are constructed for different values of the parameter $a^2$, which is related to the curvature of the scalar manifold. The behavior of solutions near the boundary is used to determine their type based on the expansion of the corresponding fake superpotential. By incorporating information on the boundary conditions, the obtained RG flows are interpreted using the holographic dictionary. Numerical solutions and plots of the fake superpotential are also provided.