Zoo of flows in a 3d gauged supergravity with periodic potential

In this paper we construct solutions with AdS/dS asymptotics for $D=3$ truncated gauged supergravity with a periodic scalar potential. In a holographic perspective, assuming Dirichlet boundary conditions, the solutions can be interpreted as deformations of 2d dual CFTs triggered by non-zero vacuum expectation values of irrelevant operators. In addition to the domain wall type solutions, we incorporated in the analysis a black string solution, which can also be interpreted as a deformation by VEV of an irrelevant operator. Generalizing the flows to finite temperature, we find that the corresponding geometries are singular but have horizons. For certain flows, we provide an analytical description near the horizon region. For an exact RG flow solution, we explicitly compute the Brown-York stress-energy tensor on a cutoff surface and show that the $T\overline{T}$ operator factorizes along the holographic RG flow. We also define an effective, scale-dependent deformation parameter $\mu(\phi)$, whose running is governed by the scalar field at the cutoff.