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We construct curved backgrounds with Euclidean signature admitting rigidsupersymmetry by using a 5d N=1 off-shell Poincare supergravity. We solve theconditions for the background Weyl multiplet and vector multiplets thatpreserve at least one supersymmetry parameterized by a symplectic Majoranaspinor, and represent the solution in terms of several independent fields. Wealso show that the partition function does not depends on the local degrees offreedom of the background fields. Namely, as far as we focus on a singlecoordinate patch, we can freely change the independent fields by combiningQ-exact deformations and gauge transformations. We also discuss realization ofseveral known examples of supersymmetric theories in curved backgrounds byusing the supergravity.

Supersymmetric backgrounds from 5d N=1 supergravity