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

Abstract

We apply the transformation of the mixing azimuthal and internal coordinate or the mixing time and internal coordinate to the 11D M theory with a stack of $\mathrm{M}2\mathrm{\text{\ensuremath{-}}}\mathrm{branes}\ensuremath{\perp}\mathrm{M}2\mathrm{\text{\ensuremath{-}}}\mathrm{branes}$, then through the mechanism of Kaluza-Klein reduction and a series of the T duality we obtain the corresponding background of a stack of $\mathrm{D}1\mathrm{\text{\ensuremath{-}}}\mathrm{branes}\ensuremath{\perp}\mathrm{D}5\mathrm{\text{\ensuremath{-}}}\mathrm{branes}$ which, in the near-horizon limit, becomes the magnetic or electric Melvin field deformed ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{T}^{4}$. We find the giant graviton solution in the deformed spacetime and see that the configuration whose angular momentum is within a finite region could have a fixed size and become more stable than the pointlike graviton, in contrast to the undeformed giant graviton which only exists when its angular momentum is a specific value and could have arbitrary size. We discuss in detail the properties of how the electric/magnetic Melvin field will affect the size of the giant gravitons. We also adopt an ansatz to find the classical string solutions which are rotating in the deformed ${S}^{3}$ with an angular momentum in the rotation plane. The spinning string and giant graviton solutions we obtained show that the external magnetic/electric flux will increase the solution energy. Therefore, from the anti-de Sitter (AdS)/conformal field theory (CFT) point of view, the corrections of the anomalous dimensions of operators in the dual field theory will be positive. Finally, we also see that the spinning string and giant graviton in the near-horizon spacetime of Melvin field deformed D5-branes background have similar properties to those in the deformed ${\mathrm{AdS}}_{3}\ifmmode\times\else\texttimes\fi{}{S}^{3}\ifmmode\times\else\texttimes\fi{}{T}^{4}$.