We discuss phantom metrics admitting Killing spinors in fake N = 2 , D = 4 supergravity coupled to vector multiplets. The Abelian U ( 1 ) gauge fields in the fake theory have kinetic terms with the wrong sign. We solve the Killing spinor equations for the standard and fake theories in a unified fashion by introducing a parameter which distinguishes between the two theories. The solutions found are fully determined in terms of algebraic conditions, the so-called stabilisation equations, in which the symplectic sections are related to a set of functions. These functions are harmonic in the case of the standard supergravity theory and satisfy the wave-equation in flat ( 2 + 1 ) -space–time in the fake theory. Explicit examples are given for the minimal models with quadratic prepotentials.
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