Symmetries of colored Khovanov-Rozansky homology

We construct an action of the positive half of the Witt algebra on colored ${\mathfrak{g}\mathfrak{l}}_N$-Khovanov-Rozansky homology and prove that this action is compatible with the functoriality of colored link homology. To establish this result, we use Bar-Natan’s framework of canopolies to formulate and prove the relevant statements at the level of tangles.