The Modification of the energy spectrum of charged particles by exotic open 4-smoothness via superstring theory

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 \BbbR4 as underlying structure of the Minkowski spacetime. The standard smoothness of \BbbR4 is shifted to the exotic

{\mathbb R}_{k}{4}

, k = 2p, p = 1, 2, \dots. This is achieved by superstring theory using gravitational backreaction induced from a strong, almost constant magnetic field on standard \BbbR4. The exact string background containing flat \BbbR4 is replaced consistently by the curved geometry of SU(2)k * \BbbR as part of the modified exact backgrounds. This corresponds to the change of smoothness on \BbbR4 from the standard \BbbR4 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 H3(SU(2), \BbbR) determines also the exotic smooth

{\mathbb R}_{k}{4}

. As the consequence we obtain that a nonzero mass-gap induced by the exotic

{\mathbb R}_{k}{4}

emerges in the spectrum.

Note:

11 pages, Revtex4-1, will appear IJGMMP Vol. 50(1), 2013

02.40.Ky
11.25.Mj
Small exotic R-4
superstring theory
sigma-models
deformation: marginal
magnetic field: high
gravitation: back reaction
space-time: Minkowski
charged particle: energy spectrum

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