Half-BPS Giants, Free Fermions and Microstates of Superstars

TL;DR

This work analyzes $1/2$-BPS states in AdS/CFT via a Hermitian matrix-model truncation, deriving explicit mappings between fermion configurations, giant gravitons, and dual-giant gravitons, and uncovering a particle-hole–like duality that equates giant and dual-giant descriptions. It computes the exact partition function $Z_N(q)=\prod_{n=1}^N(1-q^n)^{-1}$ in both pictures, showing the degeneracy grows exponentially with the total $R$-charge $\\Delta$ and that $S \approx \sqrt{\\frac{2\\pi^2}{3}}\\sqrt{\\Delta}$ in the large-$N$ limit. The exponential density suggests the single-charge superstar geometry in $AdS_5$ carries these microstates, and placing a stretched horizon reproduces the entropy up to a numerical coefficient, with analogous results in M-theory for $AdS_4\times S^7$ and $AdS_7\times S^4$. The paper further extends the duality to M-theory brane constructions, connects the microstate counting to geometric pictures, and discusses probe-brane tests and potential coarse-graining toward a full microstate-geometry description.

Abstract

We consider 1/2-BPS states in AdS/CFT. Using the matrix model description of chiral primaries explicit mappings among configurations of fermions, giant gravitons and the dual-giant gravitons are obtained. These maps lead to a `duality' between the giant and the dual-giant configurations which is the reflection of particle-hole duality of the fermion picture. These dualities give rise to some interesting consequences which we study. We then calculate the degeneracy of 1/2-BPS states both from the CFT and string theory and show that they match. The asymptotic degeneracy grows exponentially with the comformal dimension. We propose that the five-dimensional single charge `superstar' geometry should carry this density of states. An appropriate stretched horizon can be placed in this geometry and the entropy predicted by the CFT and the string theory microstate counting can be reproduced by the Bekenstein-Hawking formula up to a numerical coefficient. Similar M-theory examples are also considered.