Gauging of N=2 Supergravity Hypermultiplet and Novel Renormalization Group Flows

TL;DR

Behrndt and Cvetic perform a complete gauging of the SU(2,1) isometries for the universal N=2 hypermultiplet on the SU(2,1)/U(2) coset, parameterized by z1 and z2, and derive the full Killing prepotentials to define the most general superpotential. They then analyze Abelian gaugings, focusing on Cartan-subalgebra directions, and demonstrate that the superpotential can cross zero, yielding novel supersymmetric RG-flow/domain-wall solutions, including a flow to flat space and a c-theorem–violating flow. The authors provide explicit flow solutions, discuss fixed points and geodesic constraints, and outline how this framework can be extended to non-Abelian gaugings with vector multiplets, offering a stepping stone for more general AdS/CFT RG analyses and gravity-trapping domain walls in five-dimensional N=2 gauged supergravity.

Abstract

We provide the explicit gauging of all the SU(2,1) isometries of one N=2 supergravity hypermultiplet, which spans SU(2,1)/U(2) coset space parameterized in terms of two complex projective coordinate fields z_1 and z_2. We derive the full, explicit Killing prepotential that specifies the most general superpotential. As an application we consider the supersymmetric flow (renormalization group) equations for: (i) the flow from a null singularity to the flat, supersymmetric space-time and (ii) the flow that violates c-theorem with the superpotential crossing zero.