The giant graviton on AdS₄ x CP³ - another step towards the emergence of geometry

We construct the giant graviton on AdS_{4} x CP^{3} out of a four-brane embedded in and moving on the complex projective space. This configuration is dual to the totally anti-symmetric Schur polynomial operator \chi_{R}(A_{1}B_{1}) in the 2+1-dimensional, N = 6 super Chern-Simons ABJM theory. We demonstrate that this BPS solution of the D4-brane action is energetically degenerate with the point graviton solution and initiate a study of its spectrum of small fluctuations. Although the full computation of this spectrum proves to be analytically intractable, by perturbing around a "small'" giant graviton, we find good evidence for a dependence of the spectrum on the size, \alpha_{0}, of the giant. This is a direct result of the changing shape of the worldvolume as it grows in size.