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We first apply the transformation of mixing azimuthal and internal coordinateor mixing time and internal coordinate to the 11D M-theory with a stack NM2-branes to find the spacetime of a stack of N D2-branes with magnetic orelectric flux in 10 D IIA string theory, after the Kaluza-Klein reduction. Wethen perform the T duality to the spacetime to find the background of a stackof N D3-branes with magnetic or electric flux. In the near-horizon limit thebackground becomes the magnetic or electric field deformed $AdS_5 \times S^5$.We adopt an ansatz to find the classical string solution which is rotating inthe deformed $S^5$ with three angular momenta in the three rotation planes. Therelations between the classical string energy and its angular momenta are foundand results show that the external magnetic and electric fluxes will increasethe string energy. Therefore, from the AdS/CFT point of view, the correctionsof the anomalous dimensions of operators in the dual SYM theory will bepositive. We also investigate the small fluctuations in these solutions anddiscuss the effects of magnetic and electric fields on the stability of theseclassical rotating string solutions. Finally, we find the possible solutions ofstring pulsating on the deformed spacetimes and show that the corrections tothe anomalous dimensions of operators in the dual SYM theory are non-negative.Comment: Latex 18 pages, correct sec. 3.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Semiclassical strings in electric and magnetic field deformed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Ad</mml:mi><mml:msub><mml:mi mathvariant="normal">S</mml:mi><mml:mn>5</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>5</mml:mn></mml:msup></mml:math>spacetimes

Semiclassical strings in electric and magnetic field deformedAdS5×S5spacetimes