  According to the Axionic String Anstaz (ASA) confining flux tubes in pure
gluodynamics are in the same equivalence class as a new family of integrable
non-critical strings, called axionic strings. In addition to translational
modes, axionic strings carry a set of worldsheet axions transforming as an
antisymmetric tensor under the group of transverse rotations. We initiate a
study of integrable axionic strings at general number of space-time dimensions
$D$. We show that in the infinite tension limit worldsheet axions should be
described by a peculiar "pseudofree" theory---their $S$-matrix is trivial, but
the corresponding action cannot be brought into a free form by a local field
redefinition. This requirement fixes the axionic action to take a form of the
$O(D-2)$ Wess--Zumino--Witten (WZW) model.
