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

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