Abstract
The rotating D3-brane in the AdS5×S5 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 Pc. In this Letter we investigate the properties of the giant graviton in the electric/magnetic Melvin geometries of deformed AdS5×S5 spacetime which was obtained in our previous paper [W.-H. Huang, Phys. Rev. D 73 (2006) 026007, hep-th/0512117]. 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 analyzes show that the electric Melvin field will always render the giant graviton unstable.
Highlights
McGreevy, Susskind and Toumbas [1] found that a rotating D3-brane in the AdS5 × S5 spacetime could expand into a stable configuration which has exactly the same quantum numbers as the point-like graviton and is called as a giant graviton
The results show that the electric Melvin field always render the giant graviton unstable
The problems remain to be investigated. It is well-known that a collection of p-branes in a background field strength can undergo an expansion into a higher-dimensional p+2 spherical brane
Summary
McGreevy, Susskind and Toumbas [1] found that a rotating D3-brane in the AdS5 × S5 spacetime could expand into a stable configuration which has exactly the same quantum numbers as the point-like graviton and is called as a giant graviton. It is important to find the Yang-Mills operators corresponding to the electric/magnetic field deformed giant graviton, as those analyzed in [14] for the giant graviton in the Frolov’s three parameter generalization of the Lunin-Maldacena background [14]. The correspondence between the deformed giant graviton on the electric/magnetic field Melvin geometries and the spin chain in the deformed geometries [20], which can improve our understanding of the AdS/CFT correspondence, are deserved to be investigated. These important problems are left to further research. After taking the near-horizon limit we obtain the magnetic field deformed AdS5 × S5 background in (2.1) and electric field deformed AdS5 × S5 background in (3.1), as detailed in [15]
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