Isometries, gaugings and N=2 supergravity decoupling

TL;DR

This paper explores the decoupling limits of N=2 supergravity hypermultiplets, revealing how different spacetime geometries emerge from gauging isometries and applying rigid limits, with implications for string theory models.

Contribution

It introduces new rigid limits for N=2 hypermultiplets, linking quaternion-Kahler and hyper-Kahler geometries and distinguishing cases based on isometry types.

Findings

Rigid limits relate quaternion-Kahler and hyper-Kahler spaces with symmetry.

Different spacetime geometries (Minkowski or AdS_4) arise depending on isometry type.

Application to universal hypermultiplet in string theory context.

Abstract

We study off-shell rigid limits for the kinetic and scalar-potential terms os a single N=2 hypermultiplet. In the kinetic term, these rigid limits establish relations between four-dimensional quaternion-Kahler and hyper-Kahler target spaces with symmetry. The scalar potential is obtained by gauging the graviphoton along an isometry of the quaternion-Kahler space. The rigid limits unveil two distinct cases. A rigid N=2 theory on Minkowski or on AdS_4 spacetime, depending on whether the isometry is translational or rotational respectively. We apply these results to the quaternion-Kahler space with Heisenberg x U(1) isometry, which describes the universal hypermultiplet at type-II string one-loop.