Supersymmetric extension of the Carrollian Dp-brane

Establish a supersymmetric extension with worldvolume fermions of the electric and magnetic Carrollian Dp-brane theories obtained through the Polyakov–Kaluza–Klein reduction of the O(F^2)-truncated Dp+1-brane theory.

Background

The paper constructs electric and magnetic Carrollian Dp-brane theories by applying a single-mode Kaluza–Klein-like null reduction, a Carrollian contraction, and a Dirac constraint analysis to the Polyakov formulation of an O(F2)-truncated Dp+1-brane theory. The resulting systems retain an auxiliary worldvolume frame during constraint classification and include a worldvolume U(1) gauge sector alongside transverse embedding scalars.

The constructed theories are purely bosonic. A supersymmetric completion would need to incorporate worldvolume fermions consistently with the Carrollian limit, the reduced U(1) sector, the auxiliary-frame constraint structure, and the distinct electric and magnetic Hamiltonian families. The paper explicitly identifies this extension as an unresolved problem.

References

A supersymmetric extension with worldvolume fermions is an open problem.

— Carroll Limit of $\mathcal{O}(F^2)$ $\text{D}_p$-branes from Kaluza--Klein-like Null reduction in the Polyakov Formulation  (2609.00797 - Zeng, 1 Sep 2026) in Section 6, Conclusion

Within this interpretation, one should first implement the Carrollian limit in the field theory at finite ultraviolet cutoff and then take the cutoff to infinity. In the bulk, the finite cutoff prevents the internal sphere from collapsing before the flat-space limit is taken. Its coordinates can therefore remain real, scale in the limit, and ultimately decompactify. This suggests that the R-symmetry variables of the cutoff theory may reorganize themselves into five emergent spatial directions giving rise to a nine-dimensional Carrollian theory on $\mathscr{I}_9$, although it is unclear what form such a theory should take since there are no stable objects in IIB string theory with odd-dimensional worldvolumes.

— 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