Phantom Space-times in Fake Supergravity

TL;DR

This paper explores phantom space-times with Killing spinors in fake N=2, D=4 supergravity, revealing solutions characterized by algebraic stabilisation equations and harmonic or wave-equation functions depending on the theory.

Contribution

It introduces a unified approach to solving Killing spinor equations in both standard and fake supergravity theories, highlighting the role of algebraic stabilisation equations.

Findings

Solutions are fully determined by algebraic stabilisation equations.

In standard supergravity, functions are harmonic; in fake supergravity, they satisfy wave equations.

Explicit examples provided for minimal models with quadratic prepotentials.

Abstract

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.