Instantons and Wormholes in N=2 supergravity

In this paper, we construct Euclidean instanton and wormhole solutions in $d=4$, N=2 supergravity theories with hypermultiplets. The analytic continuation of the hypermultiplet action, involving pseudoscalar axions, is discussed using the approach originally developed by Coleman which determines the apparence of boundary terms. In particular, we investigate the conditions obtained by requiring the action to be positive-definite once the boundary terms are taken into account. The case of two hypermultiplets parameterizing the coset $G_{2,2}\mathrm{/}SU(2)\times SU(2)$ is studied in detail. Orientifold projections which reduce the supersymmetry to N=1 are also discussed.