Universal BPS Structure of Scalar Kinks in Static Geometries

TL;DR

This paper extends the BPS construction for scalar kinks to static curved spacetimes, showing that geometric factors influence zero mode existence and soliton stability, with implications for controlling solitonic properties via geometry.

Contribution

It introduces a geometric extension of the BPS framework for scalar kinks in curved backgrounds, maintaining the first-order equations while revealing geometric effects on zero modes and stability.

Findings

BPS kinks remain linearly stable in curved spacetimes.

Zero mode normalizability depends on the interplay between kink scale and curvature.

Different spacetime slicings can eliminate translational zero modes.

Abstract

We present a geometric extension of the Bogomolny-Prasad-Sommerfield (BPS) construction for scalar kinks in (1+1) dimensions embedded in static curved spacetimes. By introducing a nonminimal coupling between the scalar prepotential and the extrinsic curvature of the static foliation, the flat-space first-order Bogomolny equation remains exactly valid for arbitrary static backgrounds. As a consequence, the kink profile is unchanged, while the effective potential and vacuum structure acquire a controlled geometric dependence. We show that these curved-space BPS kinks are always linearly stable. However, the existence of the translational zero mode is not guaranteed: its normalizability depends on the competition between the intrinsic length scale of the kink and the asymptotic curvature scale of the geometry. When the geometric scale dominates, the zero mode is removed and the soliton becomes geometrically pinned, despite remaining an exact BPS solution. Explicit realizations in AdS2 demonstrate how different static slicings of the same spacetime lead to qualitatively distinct physical outcomes, ranging from preserved translational invariance to its complete removal by horizons. These results establish geometry as a precise mechanism for controlling solitonic moduli without compromising linear stability.