  In this paper we present a model where the modified Landau-like levels of
charged particles in a magnetic field are determined due to the modified
smoothness of $\mathbb{R}^{4}$ as underlying structure of the Minkowski
spacetime. Then the standard smoothness of $\mathbb{R}^{4}$ is shifted to the
exotic $\mathbb{R}_{k}^{4}$, $k=2p$, $p=1,2...$. This is achieved by
superstring theory using gravitational backreaction induced from a strong,
almost constant magnetic field on standard $\mathbb{R}^{4}$. The exact string
background containing flat $\mathbb{R}^{4}$ is replaced consistently by the
curved geometry of $SU(2)_{k}\times\mathbb{R}$ as part of the modified exact
backgrounds. This corresponds to the change of smoothness on $\mathbb{R}^{4}$
from the standard $\mathbb{R}^{4}$ to some exotic $\mathbb{R}_{k}^{4}$. The
calculations of the spectra are using the CFT marginal deformations and
Wess-Zumino-Witten (WZW) models. The marginal deformations capture the effects
of the magnetic field as well as its gravitational backreactions. The spectra
depend on even level $k$ of WZW on SU(2). At the same time the WZ term as
element of $H^{3}(SU(2),\mathbb{R})$ determines also the exotic smooth
$\mathbb{R}_{k}^{4}$. As the consequence we obtain a non-zero mass-gap emerges
in the spectrum induced from the presence of an exotic $\mathbb{R}_{k}^{4}$.
