Starting from compete UV description of QCD (in the confined phase), if we integrate out the quarks and Glueballs, in principle, we will get an effective theory of strings (QCD flux tube and not fundamental strings). This effective theory clearly exists in $D=4$. The simplest theoretical model to study such an effective theory is to consider a infinitely long string (arXiv:1302.6257), such solutions exit and are stable in known theories e.g. pure Yang-Mills in any $D$.
In the presence of such a long string the theory breaks $SO(D-1,1)$ spacetime symmetry to $SO(1,1) \times SO(D-2)$. The Nambu-Goldstone modes from this symmetry breaking are the only physical degrees of freedom on the worldsheet of this string.
In the light cone gauge, away from critical dimensions ($D=26$) the spectrum does not obey Lorentz symmetry. The Weyl anomaly we get, in the covariant formulation appears as the Lorentz anomaly in the light cone gauge.
It is claimed (e.g. in arXiv:1603.06969 section 2.1) in the static gauge $(X^0 = \tau, X^1 = \sigma)$ where $(\tau,\sigma)$ are the worldsheet coordinates. The theory is unitary and there is no anomaly. Intuitively any gauge choice should reflect the anomaly in some form. So,
Why is effective string theory without any anomaly, in the static gauge, away from critical dimensions?
