BPS Chaos

TL;DR

This paper investigates the chaotic nature of BPS black holes and related systems, finding that certain supersymmetric states exhibit weak chaos, contrasting with the strong chaos expected of finite horizon black holes, through analytic and numerical analysis.

Contribution

It provides the first detailed analysis of chaos diagnostics in BPS black hole ground states and related supersymmetric systems, revealing their weak chaotic behavior.

Findings

BPS ground states show weak chaos with a Thouless time growing as a power of N.

Finite horizon BPS black holes are expected to be strongly chaotic with a Thouless time of order one.

Chaotic states can become BPS as N decreases, potentially retaining strong chaos.

Abstract

Black holes are chaotic quantum systems that are expected to exhibit random matrix statistics in their finite energy spectrum. Lin, Maldacena, Rozenberg and Shan (LMRS) have proposed a related characterization of chaos for the ground states of BPS black holes with finite area horizons. On a separate front, the "fuzzball program" has uncovered large families of horizon-free geometries that account for the entropy of holographic BPS systems, but only in situations with sufficient supersymmetry to exclude finite area horizons. The highly structured, non-random nature of these solutions seems in tension with strong chaos. We verify this intuition by performing analytic and numerical calculations of the LMRS diagnostic in the corresponding boundary quantum system. In particular we examine the 1/2 and 1/4-BPS sectors of $\mathcal{N}=4$ SYM, and the two charge sector of the D1-D5 CFT. We find evidence that these systems are only weakly chaotic, with a Thouless time determining the onset of chaos that grows as a power of $N$. In contrast, finite horizon area BPS black holes should be strongly chaotic, with a Thouless time of order one. In this case, finite energy chaotic states become BPS as $N$ is decreased through the recently discovered "fortuity" mechanism. Hence they can plausibly retain their strongly chaotic character.