Holographic Thermodynamic Signatures of Simpson--Visser--AdS Black Holes

We study a Simpson–Visser regularization of the four-dimensional Schwarzschild–anti–de,Sitter (SV–AdS) black hole, treated as the bulk dual of a planar conformal field theory (CFT) on the AdS boundary. The bulk lapse $f(r)=1-2M\mathrm{/}\sqrt{r^2+a^2}+(r^2+a^2)\mathrm{/}{\mathrm{\ell }}^2$ is regular at $r=0$ for any $a>0$, and the holographic dictionary inherits this regularity at the boundary CFT level. We derive in closed form the boundary entropy, energy, temperature, and chemical potentials, and we trace how the SV regularization parameter $a$ deforms each of them as a function of the horizon radius. For $\text{tila}<{\text{tila}}_c=1\mathrm{/}\sqrt{24}\approx 0.204$ the bulk temperature develops a van der Waals–type small/intermediate/large branch structure and the off-shell free energy supports three coexisting equilibria; the topological-vector-field analysis assigns local winding numbers $(+1,-1,+1)$ with total charge $W=+1$, matching the universality class of regular AdS black holes (Bardeen-AdS, Hayward-AdS) and distinguishing the SV-AdS family from Schwarzschild-AdS ($W=0$).