Electric/Magnetic Field Deformed Giant Gravitons in Melvin Geometry

TL;DR

This paper studies how electric and magnetic Melvin deformations affect the stability, energy, and size of giant gravitons in the $AdS_5 imes S^5$ spacetime, revealing magnetic fields can stabilize giant gravitons.

Contribution

It provides a detailed analysis of giant graviton behavior in Melvin geometries, highlighting the stabilizing effect of magnetic fields and the instability caused by electric fields.

Findings

Magnetic Melvin fields lower the energy of giant gravitons compared to point-like gravitons.

Critical angular momentum increases with magnetic flux B.

Giant graviton radius initially increases then decreases with angular momentum in magnetic fields.

Abstract

The rotating D3-brane in the $AdS_5 \times S^5$ spacetime could be blowed up to the spherical BPS configuration which has the same energy and quantum number of the point-like graviton and is called as a giant graviton. The configuration is stable only if its angular momentum was less than a critical value of $P_c$. In this paper we investigate the properties of the giant graviton in the electric/magnetic Melvin geometries of deformed $AdS_5 \times S^5$ spacetime which was obtained in our previous paper (hep-th/0512117, Phys. Rev. D73 (2006) 026007). We find that in the magnetic Melvin spacetime the giant graviton has lower energy than the point-like graviton. Also, the critical value of the angular momentum is an increasing function of the magnetic field flux $B$. In particular, it is seen that while increasing the angular momentum the radius of giant graviton is initially an increasing function, then, after it reach its maximum value it becomes a decreasing function of the angular momentum. During these regions the giant graviton is still a stable configuration, contrast to that in the undeformed theory. Finally, beyond the critical value of angular momentum the giant graviton has higher energy than the point-like graviton and it eventually becomes unstable. Our analyses show that the electric Melvin field will always render the giant graviton unstable.