Holographic Entanglement Anisotropy as a Dark Deformation RG Probe in Hyperscaling-Violating $p$-Wave Superfluids

Abstract

We study dark-sector deformations of anisotropic \(p\)-wave superfluids in hyperscaling-violating black-brane backgrounds, where the visible non-Abelian sector condenses a vector order parameter that breaks boundary spatial rotations and supplies a directional entanglement probe. Reading the strip entanglement entropy as a function of width turns this probe into a scale-resolved diagnostic: in four and five bulk dimensions, the orientation difference \(S_\perp-S_\parallel\) separates hidden couplings into scale-independent and width-running classes while filtering out isotropic dark sources entirely. Hidden-current mixing renormalizes the visible anisotropic response by a width-independent factor and strongly hybridizes the critical vector mode; a scalar gauge-kinetic portal instead reweights the radial Yang--Mills operator, so Ryu--Takayanagi surfaces of different widths sample different depths of the bulk deformation. We treat this scalar channel as a sourced boundary-value problem with a dilaton-dressed mass term, yielding a controlled short-width power law. The channel classification, the sign of each response, and the short-width exponent \(2\Delta_{\rm UV}\) are fixed by the background weights and the ultraviolet scalar falloff; the running-channel amplitude is not, since it depends on the portal normalization. We therefore state our conclusions at the level of these normalization-independent discriminants. The three-dimensional case is treated separately as an interval response.