Isometries, gaugings and N = 2 supergravity decoupling

We study off-shell rigid limits for the kinetic and scalar-potential terms of a single N = 2 hypermultiplet. In the kinetic term, these rigid limits establish relations between four-dimensional quaternion-Kähler and hyper-Kähler target spaces with symmetry. The scalar potential is obtained by gauging the graviphoton along an isometry of the quaternion-Kähler space. The rigid limits unveil two distinct cases. A rigid N = 2 theory on Minkowski or on AdS₄ spacetime, depending on whether the isometry is translational or rotational respectively. We apply these results to the quaternion-Kähler space with Heisenberg ⋉ U(1) isometry, which describes the universal hypermultiplet at type-II string one-loop.