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We apply the transformation of mixing azimuthal and internal coordinate ormixing time and internal coordinate to the 11D M-theory with a stack ofM2-branes $\bot$ M2-branes, then, through the mechanism of Kaluza-Kleinreduction and a series of the T duality we obtain the corresponding backgroundof a stack of D1-branes $\bot$ D5-branes which, in the near-horizon limit,becomes the magnetic or electric Melvin field deformed $AdS_3 \times S^3 \timesT^4$. We find the giant graviton solution in the deformed spacetime and seethat the configuration whose angular momentum is within a finite region couldhas a fixed size and become more stable than the point-like graviton, incontrast to the undeformed giant graviton which only exists when its angularmomentum is a specific value and could have arbitrary size. We discuss indetail the properties of how the electric/magnetic Melvin field will affect thesize of the giant gravitons. We also adopt an ansatz to find the classicalstring solutions which are rotating in the deformed $S^3$ with an angularmomentum in the rotation plane. The spinning string and giant gravitonsolutions we obtained show that the external magnetic/electric flux willincrease the solution energy. Therefore, from the AdS/CFT point of view, thecorrections of the anomalous dimensions of operators in the dual field theorywill be positive. Finally, we also see that the spinning string and giantgraviton in the near-horizon spacetime of Melvin field deformed D5-branesbackground have the similar properties as those in the deformed $AdS_3 \timesS^3 \times T^4$.Comment: Latex 21 pages, slightly detail calculation

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

Spinning string and giant graviton in electric/magnetic field deformed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>AdS</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>3</mml:mn></mml:msup><mml:mo>×</mml:mo><mml:msup><mml:mi>T</mml:mi><mml:mn>4</mml:mn></mml:msup></mml:math>

Spinning string and giant graviton in electric/magnetic field deformedAdS3×S3×T4