Higher-spin auxiliary-field formulations

Develop scalar auxiliary-field couplings that describe higher-spin deformations of integrable sigma models generated by higher-degree chiral invariants, and determine their auxiliary-field structure beyond the spin-2 case.

Background

The paper observes that higher-spin deformations can be introduced by coupling auxiliary fields to terms such as tr(v_+n) and tr(v_-n), rather than only to the quadratic chiral invariants relevant for stress-tensor deformations. In contrast to the spin-2 case, the resulting equations for the Lie-algebra-valued auxiliary fields are nonlinear, and the authors do not establish the corresponding scalar auxiliary-field formulation or its properties.

References

Nevertheless, it should still be possible to introduce couplings to scalar auxiliary fields that describe higher-spin deformations of these models. We leave the exploration of this interesting direction to future work.

— Integrable auxiliary field sigma model and the metric approach to $T\bar{T}$-like deformations  (2610.13501 - Baglioni et al., 9 Oct 2026) in Section 1, final paragraphs before Section 3