Abstract
We construct a new giant graviton solution on the recently constructed pp-wave geometry of the non-supersymmetric Schrödinger background. That solution exhibits an intriguing behavior as the deformation parameter of the spacetime varies. Firstly, the degeneracy between the giant and the point graviton is lifted for the benefit of the giant graviton as soon as the deformation is turned on. Secondly, when the deformation parameter exceeds a critical value the barrier separating the point from the giant graviton disappears. This suggests that the mere presence of a D3-brane leads to the spontaneous breaking of conformal invariance. We perform a detailed analysis of the full bosonic spectrum, which reveals that the deformation induces a coupling between the scalar and the gauge field fluctuations. It is exactly this coupling that keeps the giant graviton free of tachyonic instabilities. Furthermore, the giant graviton configuration completely breaks the supersymmetry of the pp-wave background, as the Kappa-symmetry analysis suggests.
Highlights
Extract information about structure constants involving non-protected operators
The giant graviton configuration completely breaks the supersymmetry of the pp-wave background, as the Kappa-symmetry analysis suggests
These non-BPS operators are dual to string states propagating on the pp-wave limit of the AdS5 × S5 background which can be obtained by focusing on the geometry around a null geodesic
Summary
We begin this section by first reviewing the pp-wave solution of the Schrodinger geometry that was presented in [29]. In order to describe Giant Graviton solutions, we need to consider the action of a probe D3-brane in the Schrodinger pp-wave background. Since this a not a priori consistent way of embedding the brane inside the ten-dimensional geometry, we need to check whether the ansatz (2.6) satisfies the equations of motion Implementing this consistency check we realize that it is true only when the parameter ν acquires the following two values ν. At the value of the deformation parameter ω m the intermediate local maximum disappears and the only extrema are the minimum at ρ0 = ρ0+ and the point graviton at ρ0 = 0, which becomes a maximum of the potential (blue dotted curve in figure 1). It is almost impossible to isolate a three-sphere inside the Schrodinger part of the geometry, wrap there a D3-brane and construct the dual Giant Graviton solution
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