Robust Finite-Momentum Instabilities in Dense Matter

The predicted extent of inhomogeneous chiral phases in effective models of quantum chromodynamics is notoriously sensitive to ultraviolet regularization. We show that this sensitivity is largely artificial. In the two-flavor Nambu--Jona-Lasinio model, conventional implementations of three-dimensional cutoff, Pauli--Villars, and proper-time regularization produce strongly different finite-momentum instability regions. Once ultraviolet regulators are restricted to genuinely divergent vacuum contributions, however, all three prescriptions yield nearly identical stability diagrams. Both the onset of the moat regime and the subsequent finite-momentum instability become quantitatively robust. The apparent scheme dependence originates from regulating ultraviolet-finite medium contributions associated with the Fermi-surface response. Our results identify spatially modulated chiral correlations as a genuine property of the dense medium rather than an artifact of the ultraviolet prescription.