Curved BPS domain walls and RG flow in five dimensions

TL;DR

The paper establishes the existence and structure of curved BPS domain walls in five-dimensional $N=2$ gauged supergravity with vector and hypermultiplets, linking them to holographic RG flows on curved 4D spacetimes. It derives the curved-wall BPS flow equations for the warp factor and all scalar sectors, analyzes integrability and the associated energy functional, and identifies a consistency condition $\Gamma(\phi,q)=\gamma(r)$ that must hold when vector multiplets are present. The authors interpret these curved walls as dual RG flows with a monotonic $c$-function $C(r) \propto W^{-3}$ and beta-functions $\beta^{\Lambda}=\gamma^{-1}W^{-1}\phi'^{\Lambda}$, showing curvature on the wall acts as an infrared regulator and can modify fixed-point structure. An explicit curved-wall solution is constructed in the universal hypermultiplet model, illustrating how curvature and quaternionic geometry enter the flow and demonstrating regimes in which curved solutions exist or are truncated by the curvature through zeros of $\gamma$. These results generalize flat-wall analyses and provide a concrete gravitational description of RG flows in curved backgrounds.

Abstract

We determine, in the context of five-dimensional ${\cal N}=2$ gauged supergravity with vector and hypermultiplets, the conditions under which curved (non Ricci flat) supersymmetric domain wall solutions may exist. These curved BPS domain wall solutions may, in general, be supported by non-constant vector and hyper scalar fields. We establish our results by a careful analysis of the BPS equations as well as of the associated integrability conditions and the equations of motion. We construct an example of a curved BPS solution in a gauged supergravity model with one hypermultiplet. We also discuss the dual description of curved BPS domain walls in terms of RG flows.

Figures (4)

• Figure 1: Left: $T^2 (h)$. Right: $T^2(r)$ for the value $\Lambda =1$.
• Figure 2: $h(r)$ (left) and $f(r)$ (right) for the value $\Lambda =1$.
• Figure 3: ${\rm e}^{U(r)}$ for the value $\Lambda =1$.
• Figure 4: The two real solutions of $h^5 -h^6 = \Lambda^{-6}$ occur where the horizontal line $\Lambda^{-2}$ intersects $T^2(h)$.