Vibration modes of giant gravitons in the background of dilatonic D-branes

We consider the perturbation of giant gravitons in the background of dilatonic D-branes whose geometry is not of a conventional form of AdSm×S. We use the quadratic approximation to the brane action to investigate their vibrations around the equilibrium configuration. We found the normal modes of small vibrations of giant gravitons and these vibrations are turned out to be stable. Electronic address: [email protected] Electronic address: [email protected] 1 Recently stable extended brane configurations in some string theory background, called giant gravitons, attracted interests in connection with the stringy exclusion principle. Myers [1] found that certain D-branes coupled to RR potentials can expand into higher dimensional branes. McGreevy, Susskind and Toumbas [2] have shown that a massless particle with angular momentum on the S part of AdSm×S spacetime blows up into a spherical brane of dimensionality n−2. Its radius increases with increasing angular momentum. The maximum radius of the blown-up brane is equal to the radius of the sphere that contains it since the angular momentum is bounded by the radius of S. This is a realization of the stringy exclusion principle [3] through the AdS/CFT correspondence [4]. Later it was shown that the same mechanism can be applied to spherical branes on the AdS part. [5,6]. However, they can grow arbitrarily large since there is no upper bound on the angular momentum. To solve this puzzle, instanton solutions describing the tunneling between the giant gravitons on the AdS part and on the S part were introduced [5,7]. A magnetic analogue of the Myers effect was investigated by Das, Trivedi and Vaidya [8]. They suggested that the blowing up of gravitons into branes are also possible on some backgrounds other than AdSm × S spacetime Perturbations of the giant gravitons around their equilibrium configuration were studied by Das, Jevicki and Mathur [9]. Using quadratic approximation to the action, they computed the natural frequency of the normal mode for giant gravitons in AdSm × S spacetime for both cases when gravitons are extended in AdS space and they are extended on the sphere. Frequencies are related to the curvature scale of the background and are independent of the radius of the brane itself. These modes are believed to play an important role in the study of black holes within the string theory context. We cannot explain the microscopic properties of a black hole if it is regarded as a point singularity. But in string theory, a pointlike singularity can be replaced by an extended brane, and vibration modes of the brane can be used to study the microscopic entropy [10] and Hawking radiation [11]. In this paper, we will study the vibration mode of giant gravitons in the near-horizon geometry of dilatonic D-brane background. As a concrete example, we will consider the case 2 when a probe p-brane wraps the transverse direction of S in the near-horizon geometry of D(6−p) branes [8]. Since the background geometry is not exactly of the form AdSm×S, it would be very interesting to study the fluctuation analysis around this configuration. Consider a probe Dp-brane moving in the near-horizon geometry of extremal N D(6−p)branes. The bacground metric is given by ds = gttdt 2 + 6−p