Giant Hedge-Hogs: Spikes on Giant Gravitons

TL;DR

This work analyzes giant gravitons on the maximally supersymmetric IIB plane-wave, deriving a low-energy light-cone Hamiltonian that yields a leading $U(1)$ gauge theory on $\mathbb{R}\times S^3$. The authors identify two zero-energy vacua (including a finite-radius three-sphere with $R^2 = \mu p^+ g_s$) and compute the full spectrum of bosonic and fermionic fluctuations, showing they organize into short multiplets of the $PSU(2|2)\times PSU(2|2)\times U(1)$ algebra. They include gauge-field dynamics, obtain photon spectra, and introduce BIGGons—BIon-like spike solutions corresponding to open strings piercing the giant graviton—with explicit dipole configurations, energy scaling, and half-BPS status. These results provide a two-dimensional worldsheet boundary description of giant gravitons and suggest a link to BMN gauge theory parameters via an effective coupling $g_{\text{eff}}$, while pointing toward a fuzzy $S^3$ framework for quantization and a richer non-Abelian generalization for coincident giants. The work thus connects brane polarizations in plane-wave backgrounds to open-string probes, Nambu-bracket quantization, and potential holographic realizations of plane-wave string theory.

Abstract

We consider giant gravitons on the maximally supersymmetric plane-wave background of type IIB string theory. Fixing the light-cone gauge, we work out the low energy effective light-cone Hamiltonian of the three-sphere giant graviton. At first order, this is a U(1) gauge theory on R x S^3. We place sources in this effective gauge theory. Although non-vanishing net electric charge configurations are disallowed by Gauss' law, electric dipoles can be formed. From the string theory point of view these dipoles can be understood as open strings piercing the three-sphere, generalizing the usual BIons to the giant gravitons, BIGGons. Our results can be used to give a two dimensional (worldsheet) description of giant gravitons, similar to Polchinski's description for the usual D-branes, in agreement with the discussions of hep-th/0204196.

Figures (4)

• Figure 1: Two dipole configurations. The left one has an interpretation of two fundamental strings extending off the giant graviton to infinity. The configuration on the right is unstable and has no such string interpretation. The sign of the charges are indicated and the arrows denote the direction of flux of the electric field.
• Figure 2: A quadrapole configuration of charges and the associated fundamental strings on the giant graviton.
• Figure 3: A generic giant graviton with multiple spikes, suggesting the hedge-hog title.
• Figure 4: Two giant gravitons of different radii, connected by "strings". In the limit that the radii are equal and the giant gravitons become coincident, the gauge symmetry of the worldvolume theory is enhanced.