Validate the HHLL-to-LLLL identity for non-BPS multiparticle operators

Establish whether the identity relating the small-parameter expansion of the classical supergravity HHLL correlator to the tree-level connected correlators of finite-particle non-BPS operators applies when the constituent is a descendant of a chiral primary, particularly when the resulting multiparticle states preserve no supersymmetry.

Background

The paper proposes that the light limit of a heavy-heavy-light-light correlator computed in classical supergravity encodes the tree-level connected part of a four-point correlator containing two finite-particle operators and two light operators. This relation is well motivated and has been verified for half-BPS multiparticle states, but non-BPS multiparticle operators are defined through singular OPE limits and acquire anomalous dimensions, making the extension nontrivial.

The authors test the proposed identity for a particular non-BPS double-particle operator in AdS3 and find agreement for its anomalous dimension. That calculation provides evidence rather than a general proof, so the applicability of the identity to descendants and more general nonsupersymmetric multiparticle states remains unresolved.

References

Whether the identity eq:CHsugrasmallalpha applies also when $\mathcal{O}$ is a descendant of a CPO, and especially in cases in which the multi-particle states, $(\mathcal{O}n)$, do not preserve any supersymmetry, is still unverified and far from obvious; in particular, subtleties might arise from the singular OPE limit that is implied in the definition of the multi-particle operators (see eq:nonBPSOPE).

eq:CHsugrasmallalpha:

CHsugra(z,zˉ;α)=∑n=0α2nn! cn Cn(c)(z,zˉ) ,\mathcal{C}_H^\mathrm{sugra}(z,{\bar z};\alpha)=\sum_{n=0}\frac{\alpha^{2n}}{n!}\,c^n\,\mathcal{C}_n^{(c)}(z,{\bar z})\,,

eq:nonBPSOPE:

O1(y)O2(x)=∣x−y∣Γ12 (O1O2)(x)+…withΓ12=γ12c+O(c−2) .\mathcal{O}_1(y) \mathcal{O}_2(x) = |x-y|^{\Gamma_{12}}\,(\mathcal{O}_1 \mathcal{O}_2)(x) + \ldots\quad \mathrm{with}\quad \Gamma_{12}=\frac{\gamma_{12}}{c}+O(c^{-2})\,.

— Holographic correlators with non-supersymmetric multi-particle states  (2609.20534 - Giorgi et al., 17 Sep 2026) in Section 2, subsection “Correlators with non-BPS multiparticle operators”