Hypermultiplets, domain walls and supersymmetric attractors

TL;DR

This work develops a general framework for supersymmetric flows in five-dimensional ${\cal N}=2$ gauged supergravity with vector and hypermultiplets, expressing the dynamics through a single superpotential $W$ built from dressed quaternionic prepotentials and establishing algebraic attractor equations for AdS critical points. It derives the full set of BPS domain-wall equations, analyzes RG-flow properties, and shows how enhancement of supersymmetry at fixed points leads to tractable algebraic conditions for vacua. The authors present explicit two-model realizations: (i) the universal hypermultiplet (with or without a vector) and (ii) a vector-hypermultiplet system that reproduces the Freedman-Gubser-Pilch-Warner (FGPW) flow as an ${\cal N}=2$ truncation of an ${\cal N}=8$ configuration, including an explicit embedding and interpretation of IR/UV directions and R-symmetry mixing along the flow. These results illuminate moduli stabilization and RG flows in holography, propose new avenues for Randall–Sundrum-type constructions within 5D supergravity, and suggest deeper links to higher-dimensional string/M-theory realizations.

Abstract

We establish general properties of supersymmetric flow equations and of the superpotential of five-dimensional N = 2 gauged supergravity coupled to vector and hypermultiplets. We provide necessary and sufficient conditions for BPS domain walls and find a set of algebraic attractor equations for N = 2 critical points. As an example we describe in detail the gauging of the universal hypermultiplet and a vector multiplet. We study a two-parameter family of superpotentials with supersymmetric AdS critical points and we find, in particular, an N = 2 embedding for the UV-IR solution of Freedman, Gubser, Pilch and Warner of the N = 8 theory. We comment on the relevance of these results for brane world constructions.

Figures (4)

• Figure 1: Contours of constant $W$ in the plane $(\tau ,\sigma )$ with $V=1 -\tau^2$, $\theta =0$, for $\alpha_1=\alpha_2=0$, $\alpha_3=\sqrt{6}$, and $\beta =2\sqrt{6}$.
• Figure 2: $W$ as a function of $\xi$ along the line (\ref{['line']}), for $\alpha_1=\alpha_2=0$, $\alpha_3=\sqrt{6}$, and $\beta =2\sqrt{6}$. Note that the apparent singular point at $\xi =\pm\sqrt{2/3}=0.82$ is in fact just a regular point, as $W$ is the norm of a vector. We indicate the corresponding values of $x^5$ for the flow.
• Figure 3: Graph of the warp factor $a(x^5)=e^A$ for the values $\alpha=\sqrt{6}$ and $\beta =2\sqrt{6}$.
• Figure 4: Contours of constant $W$ in the plane $(\mathop{\rm Re}\nolimits z_1,\mathop{\rm Re}\nolimits z_2)$ for $\alpha_1=\sqrt{3/2}$ and $\beta=2\sqrt{3/2}$ (left) and for $\alpha_1=\beta=\sqrt{3/2}$ (right).