Interactions of spin‑2 and higher‑spin sectors and their backreaction on the AdS3 geometry

Develop the interacting theory for the spin‑2 and higher‑spin composite sectors derived from the Gross–Neveu model and compute the resulting corrections to the emergent AdS3 geometry beyond the spin‑1 approximation.

Background

The construction derives an infinite tower of higher‑spin composites propagating on AdS3, with the spin‑1 sector establishing the background geometry and dictionary. Linearised results are given for the spin‑2 sector.

However, a full treatment of interactions among higher‑spin fields—and how these interactions backreact on or correct the emergent AdS3 geometry—has not yet been carried out. The authors explicitly flag this as an open direction.

References

Open directions. Several directions remain open, each connected to a specific result derived here. The spin-2 and higher-spin sectors derived in Section 2 await a full treatment of their interactions and the resulting corrections to the AdS3 geometry beyond the spin-1 approximation.

— Emergent strings, holography, and cosmology from four-fermion interactions: a bottom-up derivation of AdS/CFT, dS/CFT, and $w_{1+\infty}$  (2603.27824 - Haddad, 29 Mar 2026) in Section 14 (Open directions)

The geometric result concerns classical fields. The index result is an exact statement about protected coefficients. Tests of the full interacting dynamics remain open.

— ABJM to BMN in a Double Scale Limit: Indices and Bubbling Geometries  (2609.24649 - Du, 21 Sep 2026) in Section 1, Introduction

Whether such a construction can reproduce even a restricted form of gravitational backreaction remains an open question, but would represent a step toward encoding gravitational dynamics itself.

— Black hole radial geometry from a quantum spin chain  (2610.10504 - Khanikati, 7 Oct 2026) in Discussion and outlook