Bent BPS domain walls of D=5 N=2 gauged supergravity coupled to hypermultiplets

TL;DR

This paper studies bent (AdS) BPS domain walls in $D=5$ $N=2$ gauged supergravity coupled to hypermultiplets. It derives the full set of first‑order Killing spinor equations for the metric, hypermultiplet scalars, and the $SU(2)$ projector, showing that a nonzero covariant derivative of the projector, proportional to the wall’s negative cosmological constant $oldsymbol{ abla}_{ ext{transverse}}oldsymbol{ heta} eq0$, is essential for curved walls, and proves that solutions of these Killing spinor equations satisfy the equations of motion. It then constructs explicit analytic bent-wall solutions using the universal hypermultiplet, in which two scalars run and the transverse direction is cut off at a finite value determined by $|oldsymbol{ ext{lambda}}|$, illustrating how curvature acts as a natural UV/IR regulator. Two concrete models are presented (Model I and Model II), each with a distinct parametrization of the universal hypermultiplet coset and yielding a curvature‑induced cutoff while recovering known M‑theory embeddings in the flat-wall limit. These results advance understanding of gravity trapping and RG flow geometries in five-dimensional gauged supergravity with hypermultiplets.

Abstract

Within D=5 N=2 gauged supergravity coupled to hypermultiplets we derive consistency conditions for BPS domain walls with constant negative curvature on the wall. For such wall solutions to exist, the covariant derivative of the projector, governing the constraint on the Killing spinor, has to be non-zero and proportional to the cosmological constant on the domain walls. We also prove that in this case solutions of the Killing spinor equations are solutions of the equations of motion. We present explicit, analytically solved examples of such domain walls, employing the universal hypermultiplet fields. These examples involve the running of two scalar fields and the space-time in the transverse direction that is cut off at a critical distance, governed by the magnitude of the negative cosmological constant on the wall.