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We study the geodesic distance induced by right-invariant metrics on thegroup $\operatorname{Diff}_c(M)$ of compactly supported diffeomorphisms of amanifold $M$, and show that it vanishes for the critical Sobolev norms$W^{s,n/s}$, where $n$ is the dimension of $M$ and $s\in(0,1)$. This completesthe proof that the geodesic distance induced by $W^{s,p}$ vanishes if $sp\le n$and $s<1$, and is positive otherwise. The proof is achieved by combining thetechniques of two recent papers --- [JM19] by the authors, which treated thesub-critical case, and [BHP18] of Bauer, Harms and Preston, which treated thecritical 1-dimensional case.

Geodesic distance for right-invariant metrics on diffeomorphism groups: critical Sobolev exponents