Semiclassical Strings in Electric and Magnetic Fields Deformed $AdS_5 \times S^5$ Spacetimes

TL;DR

This paper studies classical string solutions in deformed $AdS_5 imes S^5$ spacetimes with electric and magnetic fields, revealing how these fields increase string energy and affect dual gauge theory operator dimensions.

Contribution

It constructs and analyzes classical string solutions in electric and magnetic field-deformed $AdS_5 imes S^5$, exploring their energies, stability, and implications for dual SYM theory.

Findings

Magnetic and electric fluxes increase string energy.

External fields lead to positive corrections in anomalous dimensions.

Fields influence stability and pulsating solutions of strings.

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 $AdS_5 \times S^5$. 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.