SciPost Submission Page
BPS Chaos
by Yiming Chen, Henry W. Lin, Stephen H. Shenker
Submission summary
| Authors (as registered SciPost users): | Yiming Chen |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2407.19387v2 (pdf) |
| Date submitted: | 2024-10-28 03:33 |
| Submitted by: | Chen, Yiming |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1. Provides a concrete, computable, implementation of the LMRS proposal for determining chaos in BPS states.
2. Uses a range of techniques, different approaches and theories to produce a coherent, compelling picture of their claim that 1/2 and 1/4 BPS states do not have strong chaos.
3. Gives new insight into the nature of extremal black holes and their relation to horizonless microstate geometries.
4. Authors provide access to code and numerical data.
Report
In this work the authors consider quantum chaos in the context of supersymmetric gauge theory and holography. They propose that the presence of chaos in a subspace of BPS states can be detected by computing the statistical properties of the spectrum of operators projected into the subspace. They perform explicit analytical and numerical computations for scalar 1/2- and 1/4-BPS operators in N=4 SYM. They produce evidence for the absence of strong chaos in these sectors while arguing that strong chaos should appear in the 1/16-BPS sectors, in particular for the "fortuitous" operators which are BPS at only a specific value of the rank of the gauge group.
They similarly show the absence of strong chaos in the two-charge sector of the D1-D5 CFT at zero coupling. By means of the holographic duality, this provides evidence for the conjecture that BPS states corresponding to horizonless microstate geometries are distinct from chaotic macroscopic black holes.
The work is novel, of significant interest, carefully computed with multiple checks and well written. It is clearly suitable for publication.
Requested changes
1. This is not necessary for publication, but it may be useful if the authors can provide clarification on the following. The authors seem to find that, for certain simple operators in both the 1/2 and 1/4-BPS sectors of N=4 SYM, the statistics are not only not chaotic, that is Wigner-Dyson, but Poisson. While this is of course perfectly consistent with the absence of strong chaos, it seems to raise the question of whether is there a notion of integrability in these sectors of the non-planar theory? Is there a reason to believe this is a merely a mirage?
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Report
This paper tackles an important problem about black hole microstates: the distinction between typical microstates of black holes and those of smooth horizonless geometries. It conjectures that within the BPS subspace, the former exhibits strong chaos while the latter is, at most, weakly chaotic. Supporting this conjecture, the paper presents evidence by applying the LMRS diagnostic of chaos to the 1/2 and 1/4 BPS sectors in N=4 SYM and the 1/2 BPS sector in the D1-D5 CFT. Furthermore, it suggests a potential connection between chaos in the BPS and non-BPS sectors via an analytic continuation of N.
I recommend the publication of this paper after the following points are addressed:
1. On page 23, the author makes the assumption: "The Thouless time of the special banded matrix we are studying can be bounded below by the Thouless time of a banded random matrix of a similar shape." The author should clarify what is meant by a “special banded matrix.” This bound cannot universally apply to all banded matrices, as any Hermitian matrix can be transformed into a banded matrix through diagonalization using a unitary transformation.
2. In Section 6, the author applies the LMRS diagnostic to the half-BPS states in the T^4 symmetric orbifold, projecting the twist operator (6.26) onto the subspace of half-BPS states. Since (6.26) is the operator that deforms the D1-D5 CFT away from the free orbifold point, the author should clarify the distinction between their computation and the computation of the anomalous dimension and mixing matrix in the half-BPS sector. This clarification is important because the half-BPS sector is protected under such a deformation.
Recommendation
Ask for minor revision