Holographic (AdS/QCD) models can only predict the masses of multi-quark bound states once the scaling dimension of the corresponding QCD operator is known at each scale, because the holographic dictionary fixes the bulk field mass from that dimension. Evans and Ward (Phys. Rev. D 108, 026018, 2023) showed that feeding in the one-loop anomalous dimension, extrapolated into the non-perturbative infrared, substantially improves holographic predictions for the nucleon and strange baryons and yields a uuddssuuddss sexaquark mass near 1.75 GeV — low enough to be stable and a dark-matter candidate — but the result depends entirely on an uncontrolled extrapolation, since the true non-perturbative running of multi-quark operator dimensions in QCD is unknown and the one-loop factorization γOn=−nα/π\gamma_{\mathcal{O}_n}=-n\alpha/\pi is expected to break down beyond one loop. The open problem is to determine, or build a controlled model of, the infrared running of multi-quark operator dimensions in QCD and to derive the corresponding bulk-mass relation from a controlled holographic construction, thereby establishing whether the holographic evidence for a stable sexaquark — and the improved baryon mass fits — survives.

Background

Gauge/gravity duality (holography) maps a strongly coupled gauge theory onto a weakly coupled gravitational theory in one higher dimension; 'AdS/QCD' denotes bottom-up models that apply this idea to quantum chromodynamics (QCD) by placing bulk fields in five-dimensional anti-de Sitter (AdS) space, with the radial coordinate acting as an energy scale. In these models each QCD operator corresponds to a bulk field whose mass is fixed by the operator's scaling dimension through the holographic dictionary (for a scalar, m2=Δ(Δ−4)m^2=\Delta(\Delta-4) in units of the AdS radius). 'Hard wall' models cut off the geometry abruptly to generate a mass gap; more refined 'Dynamic AdS/QCD' models (in the spirit of the D3/probe-D7 brane system, a top-down string construction with flavor branes) let the mass gap emerge dynamically: the anomalous dimension γ\gamma of the quark bilinear qˉq\bar{q}q grows toward the infrared, and when it reaches 1 the bulk scalar mass violates the Breitenlohner–Freedman (BF) stability bound of AdS space, driving the sigma meson tachyonic and triggering chiral symmetry breaking — the dynamical mechanism by which quark condensates form.

The anomalous dimension of an operator measures how its scaling dimension d=d0+γd=d_0+\gamma changes with renormalization scale; in perturbation theory it is computable order by order in the strong coupling α\alpha. At one loop, a color-singlet operator built from nn quark fields has γOn=−nα/π\gamma_{\mathcal{O}_n}=-n\alpha/\pi: the running factorizes into a sum over the individual quark legs. Evans and Ward (2023) incorporated this one-loop running — extrapolated into the strongly coupled infrared where perturbation theory is invalid — for the three-quark baryon operator and the six-quark scalar operator. The lowered infrared dimensions reduce the bulk masses and bring the holographic nucleon, Λ\Lambda, and Ξ\Xi masses close to their measured values; applied to the uuddssuuddss 'sexaquark' (a hypothesized deeply bound, flavor-singlet six-quark state, historically discussed as the H dibaryon when viewed as a ΛΛ\Lambda\Lambda molecule; if its mass lies below roughly 2 GeV it cannot decay strongly and has been proposed as a stable relic and dark-matter candidate), the same running yields a mass of about 1.75 GeV, inside the stable window.

The authors themselves stress, however, that these conclusions rest on uncontrolled inputs: the one-loop factorization is expected to break down beyond one loop, so operator-specific infrared dimensions and splittings are undetermined; the extrapolation of the running into the non-perturbative regime has no controlled derivation (the same ansatz would give an equally low mass to a di-neutron, contradicting experiment); the constituent-weighted flavour mixing and the r2→r2+L2r^2\to r^2+L^2 deformation of the AdS radius are phenomenological, imported from top-down brane constructions rather than derived for QCD; and the leading large-NcN_c (number of colors) approximation omits pion-cloud and other meson-loop corrections. Lattice QCD — the numerical simulation of the theory directly — has studied the strangeness S=−2S=-2 two-baryon sector near physical quark masses (finding only weak ΛΛ\Lambda\Lambda attraction and no bound dibaryon), but this probes the molecular, not compactly bound, regime, and direct lattice results for the deeply bound six-quark channel at physical masses are not available. Meanwhile theoretical estimates of the sexaquark mass across methods span roughly 1.2 GeV to above 2.2 GeV, straddling the stability bound, so the question is genuinely unsettled.

Problem Statement

Determine the infrared, non-perturbative running of the scaling dimensions of multi-quark operators in QCD — in particular the three-quark baryon operator and the flavor-singlet six-quark operator uuddssuuddss — or produce a controlled model of that running, and derive from a controlled holographic construction the relation between the bulk field masses and the running operator dimensions. Here 'controlled' denotes a construction with an identified expansion parameter whose neglected corrections can be estimated, rather than a tuned or fitted infrared ansatz. The overarching objective is to decide whether the holographic spectroscopy of Evans and Ward is robust: specifically, whether the improved nucleon, Λ\Lambda and Ξ\Xi mass predictions and the prediction of a stable, deeply bound sexaquark with mass below roughly 2 GeV survive once the uncontrolled extrapolation of the one-loop anomalous dimension γOn=−nα/π\gamma_{\mathcal{O}_n}=-n\alpha/\pi into the non-perturbative regime is replaced by the true infrared running — or whether operator-specific non-perturbative effects (including beyond-one-loop splittings between operators with different color-flavor-spin structure, and subleading large-NcN_c effects such as pion-cloud corrections) destabilize those conclusions. A resolution of this objective requires both a controlled infrared operator-dimension profile and the resulting multi-quark bound-state spectrum with its consequences for the sexaquark stability window.

References

  1. Nick Evans, Matthew Ward (2023), Running anomalous dimensions in holographic QCD: From the proton to the sexaquark, Phys. Rev. D 108, 026018, DOI: 10.1103/PhysRevD.108.026018, arXiv:2304.10816, https://arxiv.org/abs/2304.10816
  2. Glennys R. Farrar (2022), A Stable Sexaquark: Overview and Discovery Strategies, arXiv:2201.01334, https://arxiv.org/abs/2201.01334
  3. Glennys R. Farrar, Zihui Wang (2023), Constraints on long-lived di-baryons and di-baryonic dark matter, arXiv:2306.03123, https://arxiv.org/abs/2306.03123
  4. Glennys R. Farrar, Nico Wintergerst (2023), Wave function of the sexaquark or compact H-dibaryon, J. High Energy Phys. 12 (2023) 099, DOI: 10.1007/JHEP12(2023)099, arXiv:2310.05194, https://arxiv.org/abs/2310.05194
  5. Kenji Sasaki, Sinya Aoki, Takumi Doi, Shinya Gongyo, Tetsuo Hatsuda, Yoichi Ikeda, Takashi Inoue, Takumi Iritani, Noriyoshi Ishii, Takaya Miyamoto, Keiko Murano (HAL QCD Collaboration) (2017), Baryon interactions from lattice QCD with physical masses — S=-2 sector —, PoS(LATTICE2016)116, DOI: 10.22323/1.256.0116, arXiv:1702.06241, https://arxiv.org/abs/1702.06241
  6. Kenji Sasaki, Sinya Aoki, Takumi Doi, Shinya Gongyo, Tetsuo Hatsuda, Yoichi Ikeda, Takashi Inoue, Takumi Iritani, Noriyoshi Ishii, Keiko Murano, Takaya Miyamoto (HAL QCD Collaboration) (2020), ΛΛ and NΞ interactions from lattice QCD near the physical point, Nucl. Phys. A 998 (2020) 121737, DOI: 10.1016/j.nuclphysa.2020.121737, arXiv:1912.08630, https://arxiv.org/abs/1912.08630
  7. M. C. Gordillo (2026), Sexaquarks and H dibaryons in the uuddss system: a comparison within a constituent quark model, arXiv:2604.18174, https://arxiv.org/abs/2604.18174
  8. Marianne Moore, Tracy R. Slatyer (2024), Cosmology and terrestrial signals of sexaquark dark matter, Phys. Rev. D 110, 023515, DOI: 10.1103/PhysRevD.110.023515, arXiv:2403.03972, https://arxiv.org/abs/2403.03972
  9. Marianne Moore, Stefano Profumo (2026), Nonthermal production of sexaquark dark matter, Phys. Rev. D 113, 095007, DOI: 10.1103/97bv-cf91, arXiv:2512.14838, https://arxiv.org/abs/2512.14838
  10. Mahboubeh Shahrbaf, Prashant Thakur, Davood Rafiei Karkevandi (2025), Probing strange dark matter through f-mode oscillations of neutron stars with hyperons and quark matter, J. Cosmol. Astropart. Phys. (2026) 03, 017, DOI: 10.1088/1475-7516/2026/03/017, arXiv:2510.08115, https://arxiv.org/abs/2510.08115