Question

When to trust Holography?

Answer 1

AdS/CFT correspondence allows us to compute nn-point functions of a CFT by means of solving on-shell gravitational action in anti-de Sitter space. If I understand correctly, considering classical fields in the bulk gives rise to a scale-less theory (CFT) on the boundary, which essentially describes certain fixed point. Here's what I don't understand:

Consider a holographic superconductor for instance. When the vev of the scalar field is plotted against temperature it mimics the behavior of the superconducting order parameter. The critical point is when T=TcT=Tc. Other than that, either sides of TcTc have some associated scale (the gap or the fermi momentum). So can we trust the entire plot of the vev as something which correctly reproduces the behavior of the order parameter, or it's just around TcTc? I don't understand how can scale-full physics emerge from such calculations. Clearly, I'm misunderstanding something; any help will be appreciated.