Wilson loops in exact holographic RG flows at zero and finite temperatures

We study rectangular timelike Wilson loops at long distances in the exact renormalization group flow in the context of the holographic duality. We consider the five-dimensional holographic model with an exponential dilaton potential. To probe the renormalization group flow backgrounds at zero and finite temperatures, we calculate the minimum surfaces of the corresponding string worldsheets. We show that a holographic renormalization group flow at $T=0$ mimicking the QCD behavior of the running coupling has a confining phase at long distances, while the renormalization group flow with an anti-de Sitter ultraviolet fixed point is nonconfining.