Field-Theoretic Origin of the Late-Time Rise of the ABJM Spectral Form Factor

Develop a first-principles field-theoretic understanding of the spectral correlations responsible for the late-time rise of the spectral form factor in ABJM theory, and ascertain the role of states beyond the 1/12-BPS sector counted by the current superconformal index in producing an eventual plateau.

Background

The analysis shows that, after an early-time decay, the spectral form factor in ABJM is stabilized by multi-cut saddles, with larger K becoming dominant at later times. While this accounts for the ramp-like behavior within the index framework, the precise microscopic spectral correlations driving this rise lack a first-principles field-theoretic derivation.

Because the current index counts only 1/12-BPS states, the authors suspect that including additional sectors could lead to a plateau, but the detailed mechanism and the exact classes of states responsible remain to be clarified.

References

There are several interesting open problems that we defer to future studies. First, a first-principle field-theoretic understanding of the spectral correlations responsible for the late-time rise of the SFF in ABJM remains to be developed. The superconformal index considered here only counts 1/12-BPS states; we expect that including more states should be responsible for the emergent plateau behavior.

— Supersymmetric Spectral Form Factor of ABJM Theory  (2512.11559 - Zheng, 12 Dec 2025) in Section 4 (Discussion)