Bethe Ansatz Formulation for the ABJM Superconformal Index

Establish a complete Bethe ansatz formulation for the large-N ABJM superconformal index in the Cardy-like limit, and derive the corresponding Bethe ansatz equations that capture the multi-cut saddle-point configurations introduced via shifted eigenvalues.

Background

In four-dimensional N=4 super-Yang-Mills theory, multi-cut saddle points of the superconformal index are known to be in one-to-one correspondence with Bethe roots, providing an exact Bethe ansatz formulation that preserves the 1-form center symmetry. The present work introduces analogous multi-cut saddles for the ABJM superconformal index via a shifted eigenvalue ansatz.

However, unlike the 4d case, a complete Bethe ansatz description for the ABJM index has not been worked out. The authors’ construction offers hints and motivation to identify the Bethe equations associated with these ABJM multi-cut saddles, thereby closing a gap in the exact field-theoretic understanding.

References

In the case of the ABJM SCI, however, a complete Bethe ansatz formulation has not yet been established. The shifted eigenvalue ansatz introduced here, therefore, offers a constructive hint toward deriving the corresponding Bethe ansatz equations for the ABJM SCI.

— Supersymmetric Spectral Form Factor of ABJM Theory  (2512.11559 - Zheng, 12 Dec 2025) in Section 3 (Spectral Form Factor of ABJM theory)

Whether further Bethe solutions contribute at these ranks is an open question, and one that lies outside what the present data can settle.

— Constant Maps and Exponentially Small Sectors in ABJM Bethe Observables  (2609.09273 - Hosseini, 8 Sep 2026) in Section 2, Universal twist, genus dependence, and the orbit factor; paragraph “Scope of F”