Universality across additional topological-defect symmetries

Determine whether topological defects associated with symmetries beyond the several typical cases analyzed—namely, the a0_2, U(1), and O(3) examples studied in the time-dependent Ginzburga0Landau, Grossa0Pitaevskii, holographic, and Friedmanna0Robertsona0Walker frameworks—also obey the form-factor scaling law S_f(k) cpropto k^{-(d+p+2)} in the regime k>1/xi.

Background

The paper derives and numerically verifies a proposed universal large-momentum scaling law for the defect-core form factor, S_f(k) cpropto k^{-(d+p+2)}, where d is the spatial dimension and p is the defect codimension. The verification covers selected defect types and symmetry classes, including a0_2 domain walls and kinks, U(1) vortices and vortex lines, and O(3) monopoles, across several dynamical models.

The authors explicitly identify the extension to other symmetry classes as unresolved. Establishing this would test whether the claimed dependence only on spatial dimension and codimension remains valid beyond the examples treated in the paper.