Quantize Carrollian theories

Develop a consistent quantization of Carrollian theories, thereby resolving the explicitly identified open question concerning their quantum formulation.

Background

The paper discusses candidate Carrollian boundary descriptions for the flat-space limits of AdS5×_5\timesS5^5 holographic correlators. In one proposed realization, a finite radial cutoff could lead to a nine-dimensional Carrollian theory, while other constructions involve Carrollian theories associated with analytically continued AdS5×_5\timesdS5_5.

Regardless of the precise boundary realization, the authors emphasize that quantization remains an unresolved foundational issue for Carrollian theories. This is presented as a separate open problem relevant to turning the proposed Carrollian descriptions into genuine quantum theories.

References

One may wonder whether the quantum theory possesses nontrivial zero modes or topological sectors, as well as whether there exist quantum corrections to the constraint algebra discussed in the present work.

— Carrollian axion electrodynamics  (2609.18791 - Rathi et al., 16 Sep 2026) in Section Discussion and outlook

A related difficulty is that the quantisation of Carrollian theories is still an important open question .

— Decompactification and the Flat-Space Limit of AdS$_5\times$ S$^5$ Master Correlators  (2609.05409 - Eden et al., 4 Sep 2026) in Section Discussion

Finally, quantization of the constrained Carroll D$_p$-brane phase space, including BRST or Dirac-bracket quantization of the tachyon-vacuum sector, is an interesting open problem.

— Covariant Phase Space and Carroll-Weyl $χ$ Symmetry of Carroll Non-BPS D$_p$-branes  (2609.08874 - Zeng, 8 Sep 2026) in Section 7, Conclusion

Several questions remain open. A complete quantum analysis will require a careful treatment of radial zero modes, global boundary conditions, and the full physical state space.

— Null string holography in AdS from local BRST descent  (2610.10540 - Duary et al., 7 Oct 2026) in Conclusions and Outlook