Holographic affinity: Weak gravity conjecture favors CFT thermodynamics in RN-AdS black holes with perfect fluid dark matter

We investigate the interplay between the weak gravity conjecture (WGC) and weak cosmic censorship conjecture (WCCC) for Reissner-Nordström anti-de Sitter (RN-AdS) black holes surrounded by perfect fluid dark matter (PFDM) within restricted phase space thermodynamics (RPST) and conformal field theory (CFT) thermodynamics frameworks. The WGC ensures that gravity must be the weakest force in any consistent quantum gravity theory, while the WCCC asserts that singularities from gravitational collapse must be hidden behind event horizons. We derive complete thermodynamic descriptions including mass, temperature, entropy, and free energy in both formalisms, accounting for PFDM parameterized by γ . Our analysis reveals characteristic swallowtail patterns in free energy curves, indicating van der Waals-like first-order phase transitions under specific parameter conditions. We demonstrate that the PFDM parameter γ and AdS radius ℓ play crucial roles in satisfying both conjectures. Significantly, we find that the compatibility range for WGC in CFT thermodynamics ( 3 ℓ < γ < 10 ℓ ) is substantially wider than in RPST ( 2 / 3 ℓ < γ < 5 ℓ ). This result suggests that the holographic dictionary acts as a natural filter for Swampland constraints, rendering the boundary CFT description more fundamental for consistency checks than the bulk thermodynamic variables. At critical points of black hole parameters, we verify simultaneous satisfaction of WGC and WCCC, demonstrating robustness within the critical framework. Our results provide compelling evidence that the holographic boundary description naturally encodes quantum gravity consistency conditions more efficiently than bulk thermodynamic formalisms, with perfect fluid dark matter serving as a crucial mediator enabling the reconciliation of these fundamental principles.