The giant graviton on $ Ad{S_4} \times \mathbb{C}{\mathbb{P}^3} $ — Another step towards the emergence of geometry

Abstract

Abstract:We construct the giant graviton on AdS 4 × 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 χ 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, α 0 , of the giant. This is a direct result of the changing shape of the worldvolume as it grows in size.

Open strings on D-branes from ABJM

“…These can be thought of as excitations of the giant gravitons. Giant gravitons in AdS 4 × CP 3 have been studied among others in [13,14] and references therein. Within M theory, large R-charge states and their gravity dual have been studied in [15].…”

From Schurs to giants in ABJ(M)

“…Naturally, the geometry has to generalize the dual ABJM giant graviton found in [8] that is described by two D4-branes wrapping separate CP 2 s. In ABJ the two different ranks should correspond to two different radius sizes of the CP 2 s. If we then want to attach strings into the D4s, N-strings end on the space with radius N and M-strings on the space with radius M (see Figure 2.). Moreover, from the gauge no open strings can stretch between D4-branes on the two different spaces.…”

“…In particular radiation of closed strings from giants, splitting and joining of open strings on excited gravitons and three point correlators of two heavy giants and one light graviton. After detailed analysis we put forward a prediction for the ABJ giant graviton solution that remains to be constructed and should generalize [8].…”

“…However the dictionary involving (3.2) started developing only recently [8,27]. Classical solutions dual to Schurs in AB † are a bit more involved than their counterparts in AdS 5 /CF T 4 .…”

“…In M-theory this is translated to an M5-brane wrapping two S 5 's intersecting at S 3 ⊂ S 7 and also rotating on the circle orthogonal to the compactification plane. For more details see [8,27].…”