Fayet-Iliopoulos Terms in 5D Orbifold Supergravity

TL;DR

This paper formulates boundary Fayet-Iliopoulos terms in 5D supergravity using a four-form mechanism, revealing their role in inducing kink-type scalar VEVs and mass terms in both flat and warped geometries.

Contribution

It introduces a supersymmetric formulation of boundary FI terms in 5D supergravity via a four-form multiplier, aligning with superfield results.

Findings

Boundary FI terms induce kink-type scalar VEVs.

These VEVs generate 5D kink masses for hypermultiplets.

Results are consistent across flat and warped geometries.

Abstract

We discuss a locally supersymmetric formulation for the boundary Fayet-Iliopoulos (FI) terms in 5-dimensional U(1) gauge theory on $S^1/Z_2$, using the four-form multiplier mechanism to introduce the necessary $Z_2$-odd FI coefficient. The physical consequence of the boundary FI terms is studied within the full supergravity framework. For both models giving a flat and a warped spacetime geometry, the only meaningful deformation of vacuum configuration induced by the FI terms is a kink-type vacuum expectation value of the vector multiplet scalar field which generate a 5D kink mass for charged hypermultiplet. This result for the four-form induced boundary FI terms is consistent with the one derived by the superfield formulation of 5D conformal supergravity.