Defect Approach to Giant Graviton Dynamics

TL;DR

This work develops a zero-dimensional defect framework to study light-light-heavy-heavy correlators in $\mathcal{N}=4$ SYM, focusing on giant gravitons as the heavy sector. By combining defect bootstrap with holographic input, it computes all strong-coupling four-point functions involving two maximal giant gravitons and two supergravitons of arbitrary KK level, uncovering a partially broken higher-dimensional hidden symmetry that packages these correlators into a single generating function and enabling a complete defect OPE analysis. A systematic Mellin/MeVier-Witten diagram program plus a bootstrap algorithm yields the full defect two-point data, including the complete tree-level anomalous dimensions of defect double-particle operators, and reveals how the 10d hidden conformal symmetry controls mixing and leading logarithms. The results indicate that the defect viewpoint provides a natural nonperturbative description for any LLHH correlator, as four-point blocks reduce to defect two-point blocks in the heavy limit, and set the stage for loop corrections, other backgrounds, and a robust analytic-functional formulation of LLHH dynamics.

Abstract

We develop a framework of zero dimensional defects for analyzing light-light-heavy-heavy (LLHH) correlators in conformal field theories. We specifically apply this formalism to correlators of giant gravitons in $\mathcal{N}=4$ super Yang-Mills to probe the nontrivial physics beyond planarity. By combining this framework with bootstrap techniques, we compute all four-point functions at strong coupling involving two maximal giant gravitons and two supergravitons of arbitrary dimensions. We identify a partially broken, higher-dimensional hidden symmetry -- a defect extension of 10d hidden conformal symmetry -- present at both strong and weak coupling, which allows these correlators to be packaged into a single generating function. Furthermore, we perform a systematic OPE analysis of the strong-coupling correlators, extracting the complete spectrum of anomalous dimensions for the defect-channel double-particle operators. Finally, we argue that the defect perspective provides the natural nonperturbative description for any LLHH correlator by showing that four-point conformal blocks reduce to defect two-point blocks in the heavy limit.

Figures (7)

• Figure 1: A conformal transformation moves the giant graviton insertions to $0$ and $\infty$, and maps the geodesic in the Poincaré patch into a straight line.
• Figure 2: Three types of tree-level Witten diagrams.
• Figure 3: The integral of the defect channel exchange Witten diagram splits into two parts according to different time orderings of the two inserted vertices.
• Figure 4: The two diagrams with different $\zeta$, $\bar{\zeta}$ insertion orders reorganize into two defect channel exchange Witten diagrams. The first and last diagrams of the first row correspond to the AdS diagram with the fields connected by propagators in the order $s_{k_1}$-$\zeta_l$-$\bar{\zeta}_l$-$s_{k_2}$. The middle two diagrams of the first row corresponds to the other order $s_{k_1}$-$\bar{\zeta}_l$-$\zeta_l$-$s_{k_2}$. The arrow labels the flow of the $U(1)$ charge. They reorganize into two defect channel exchange Witten diagrams in the second row. The two diagrams have internal propagators of dimensions $l +2$ and $l-2$ respectively, corresponding to exchanging the modes $\bar{\chi}_{l+1}$ and $\chi_{l-1}$.
• Figure 5: In the heavy limit, a four-point contact Witten diagram reduces to a defect two-point contact Witten diagram.