Semiclassical strings in electric and magnetic field deformedAdS5×S5spacetimes

Abstract

We first apply the transformation of mixing azimuthal and internal coordinate or mixing time and internal coordinate to the 11D M-theory with a stack N M2-branes to find the spacetime of a stack of N D2-branes with magnetic or electric flux in 10 D IIA string theory, after the Kaluza-Klein reduction. We then perform the T duality to the spacetime to find the background of a stack of N D3-branes with magnetic or electric flux. In the near-horizon limit the background becomes the magnetic or electric field deformed AdS 5 × S 5 . We adopt an ansatz to find the classical string solution which is rotating in the deformed S 5 with three angular momenta in the three rotation planes. The relations between the classical string energy and its angular momenta are found and results show that the external magnetic and electric fluxes will increase the string energy. Therefore, from the AdS/CFT point of view, the corrections of the anomalous dimensions of operators in the dual SYM theory will be positive. We also investigate the small fluctuations in these solutions and discuss the effects of magnetic and electric fields on the stability of these classical rotating string solutions. Finally, we find the possible solutions of string pulsating on the deformed spacetimes and show that the corrections to the anomalous dimensions of operators in the dual SYM theory are non-negative.

Butterfly effect and holographic mutual information under external field and spatial noncommutativity

“…The study of mutual information might also serve to determine which set of quantities are expected to be different. In this paper we extend previous method [33,34] to derive three kinds of Melvin geometry. First and second geometries describe the spacetime of a stack of N black D4-branes with magnetic or electric flux in 10 D IIA string theory.…”

On the giant magnon and spike solutions for strings onAdS3×S3

“…Recently, the rotating string with spin along various directions of S 5 was investigated by many authors in the AdS 5 × S 5 background [20,36,40,25]. As mentioned earlier, the rotating string appears as a magnon solution which is a smooth configuration or a spike solution with cusp.…”

“…Here, we will consider a string rotating on S 3 of the Melvin field deformed AdS 3 × S 3 background (see [20] for the rigidly rotating string on S 3 with no deformation). The relevant metric on R×S 3 with such a deformation is given by [36]…”

“…We have shown that for the rigidly rotating string of the two sphere, in the background of constant NS-NS B-field, there exists two limiting cases of interest. First one is the known magnon solution studied in [35,36]. The second one is the single spike solution that generalizes of the single spike solution on R×S 2 found in [20].…”

D1-brane in β-deformed background

“…This background has been conjectured to the LeighStrassler marginal deformation of N = 4 SYM. The study of properties of classical string in these backgrounds was performed in many papers, for example [20,27,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47]. Our goal is to perform similar analysis in the case of D1-brane.…”