# Isometries, gaugings and $\mathcal{N}$ = 2 supergravity decoupling

Abstract : We study off-shell rigid limits for the kinetic and scalar-potential terms of a single $\mathcal{N}$ = 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 $\mathcal{N}$ = 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-Kähler space with Heisenberg ⋉ U(1) isometry, which describes the universal hypermultiplet at type-II string one-loop.
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https://hal.archives-ouvertes.fr/hal-01554798
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Submitted on : Monday, July 3, 2017 - 6:19:01 PM
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### Citation

Ignatios Antoniadis, Jean-Pierre Derendinger, P. Marios Petropoulos, Konstantinos Siampos. Isometries, gaugings and $\mathcal{N}$ = 2 supergravity decoupling. JHEP, 2016, 11, pp.169. ⟨10.1007/JHEP11(2016)169⟩. ⟨hal-01554798⟩

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