Generalised Fayet–Iliopoulos Terms in Supergravity

Abstract: The U(1) vector multiplet theory with the Fayet–Iliopoulos (FI) term is one of the oldest and simplest models for spontaneously broken rigid supersymmetry. Lifting the FI term to supergravity requires gauged R-symmetry, as was first demonstrated in 1977 by Freedman within N = 1 supergravity. There exists an alternative to the standard FI mechanism, which is reviewed in this conference paper. It is obtained by replacing the FI model with a manifestly gauge-invariant action such that its functional form is determined by two arbitrary real functions of a single complex variable. One of these functions generates a superconformal kinetic term for the vector multiplet, while the other yields a generalised FI term. Coupling such a vector multiplet model to supergravity does not require gauging of the R-symmetry. These generalised FI terms are consistently defined for any off-shell formulation for N = 1 supergravity, and are compatible with a supersymmetric cosmological term.