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$^4$He confined in nanoporous Gelsil glass is a unique, strongly correlatedBose system exhibiting quantum phase transition (QPT) by controlling pressure.Previous studies revealed that the QPT occurs with four - dimensional (4D) XYcriticality, which appears in the zero-temperature limit of the superfluiddensity. However, the $P-T$ phase diagram also suggested that 4D XY natureappears at finite temperatures. Here, we have determined the critical exponentof the superfluid density of $^4$He in two Gelsil samples that have porediameter to be about 3 nm, using a newly developed mechanical resonatortechnique. The critical exponent $\zeta$ in the powerlaw fitting $\rho_{\mathrms} \propto \left| 1 - T/T_{\mathrm c} \right| ^{\zeta}$, where $T_{\mathrm c}$is the superfluid transition temperature, was found to be 1.0 $\pm$ 0.1 for allpressures realized in this experiment, 0.1 $<$ $P$ $<$ 2.4 MPa. This value of$\zeta$ gives a decisive evidence that the finite-temperature superfluidtransition belongs to 4D XY universality class. The emergence of the 4D XYcriticality is explained by the existence of many nanoscale superfluiddroplets, the so called localized Bose - Einstein condensates (LBECs), above$T_{\mathrm c}$. Due to the large energy cost for $^4$He atoms to move betweenthe LBECs, the phase of the LBEC order parameters fluctuates not only inspatial (3D) but imaginary time ($+1$D) dimensions, resulting in the 4D XYcriticality by a temperature near $T_{\mathrm c}$, which is determined by thefinite size of the system in the imaginary time dimension. Below $T_{\mathrmc}$, macroscopic superfluidity grows in the nanopores of Gelsil by thealignment of the phases of the LBEC order parameters. An excess dissipationpeak observed below $T_{\mathrm c}$ is well explained by this phase matchingprocess.

4D-XY Superfluid Transition and Dissipation in $^4$He Confined in Nanoporous Media