Abstract
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 ℝ4 as underlying structure of the Minkowski spacetime. The standard smoothness of ℝ4 is shifted to the exotic [Formula: see text], k = 2p, p = 1, 2, …. This is achieved by superstring theory using gravitational backreaction induced from a strong, almost constant magnetic field on standard ℝ4. The exact string background containing flat ℝ4 is replaced consistently by the curved geometry of SU (2)k × ℝ as part of the modified exact backgrounds. This corresponds to the change of smoothness on ℝ4 from the standard ℝ4 to some exotic [Formula: see text]. 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 H3( SU (2), ℝ) determines also the exotic smooth [Formula: see text]. As the consequence we obtain that a nonzero mass-gap induced by the exotic [Formula: see text] emerges in the spectrum.
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