Words to describe a black hole

TL;DR

This work reframes black hole microstate counting as a cohomology problem in the 1/16-BPS sector of $N=4$ SYM, and develops a refined, constructive enumeration of cohomology classes beyond multi-graviton states. It introduces the BPS letters/words framework and shows that the 1/16-BPS spectrum is governed by relative Lie superalgebra cohomology, with a perturbative non-renormalization theorem ensuring coupling-independence to all orders. The authors perform a comprehensive finite-N, high-derivative enumeration, obtaining evidence for a non-graviton cohomology class at $N=2$ with $E=19/2$ and exposing giant-graviton-like dip structures in finite-$N$ data, while finding that for $N=3,4$ all states are multi-graviton up to the computed range. These results strengthen the link between bulk black hole microstates and CFT operators, provide a data-rich foundation for probing microstate structure, and propose avenues—such as localization of the BPS partition function and connections to spin matrix theory—for future deeper insight into quantum gravity at the black hole threshold.

Abstract

We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.

Figures (2)

• Figure 1: Logarithmic plot of the number of 1/16-BPS states ${\bf d}_N(n)$ (dots) and the absolute-valued index $d_N(n)$ (circles) at each $n$ for $\text{SU}(N)$ and $\text{U}(N)$ gauge groups, $N = 2, 3, 4$.
• Figure 2: Logarithmic plot of the absolute-valued coefficients of $Z_N/Z_{N=\infty}$ (dots) and $I_N/I_{N=\infty}$ (circles), for $N = 2, 3, 4$.