Giant Gravitons and a Correspondence Principle

TL;DR

The paper proposes a correspondence principle linking large-charge black holes in ${\rm AdS}_{l}\times {\rm S}^{k}$ to small-charge black holes in ${\rm AdS}_{k}\times {\rm S}^{l}$ by interpreting curvature singularities as condensates of giant gravitons. It extends the Myers–Tafjord giant-graviton picture to 4D and 7D gauged supergravities, with explicit uplifting to 11D that places giant gravitons on spheres within the internal space. A central result is an exact entropy-based thermodynamic correspondence: in near-BPS limits, the entropies of the dual descriptions match when $N$ and $N_g$ are exchanged while holding the energy scale $L$ and $L\delta M$ fixed, with the giant-graviton spectrum providing a microscopic account. The work suggests a broader quantum duality where condensed giants effectively replace background branes, motivating a CFT interpretation in terms of giant-graviton operators and nonplanar dynamics, and highlighting potential instabilities and future directions for a complete microscopic formulation.

Abstract

We propose a correspondence between the physics of certain small charge black holes in AdS_k x S^l and large charge black holes in AdS_l x S^k. The curvature singularities of these solutions arise, following Myers and Tafjord, from a condensate of giant gravitons. When the number of condensed giants N_g is much greater than the number of background branes N, we propose that the system has an equivalent description in terms of N giant gravitons condensed in a background created by N_g branes. Our primary evidence is an exact correspondence between gravitational entropy formulae of small and large charge solutions in different dimensions.