On 4D, ${\mathcal{N}=2}$ deformed vector multiplets and partial supersymmetry breaking in off-shell supergravity

TL;DR

This paper explores how electric and magnetic FI terms deform off-shell vector multiplets in supergravity, leading to models with partial supersymmetry breaking and zero cosmological constant, extending previous superconformal frameworks.

Contribution

It develops a supergravity model with partial local supersymmetry breaking using magnetic FI deformations within a superconformal approach, incorporating hyper-dilaton Weyl multiplet and special-K"ahler sigma models.

Findings

Deformation of off-shell vector multiplets in supergravity is achieved.

Partial supersymmetry breaking with zero cosmological constant is realized.

The model couples hyper-dilaton Weyl multiplet to special-K"ahler sigma model.

Abstract

Electric and magnetic Fayet-Ilioupulous (FI) terms are used to engineer partial breaking of ${\mathcal{N}=2}$ global supersymmetry for systems of vector multiplets. The magnetic FI term induces a deformation of the off-shell field transformations associated with an imaginary constant shift of the triplet of auxiliary fields of the vector multiplet. In this paper, we elaborate on the deformation of off-shell vector multiplets in supergravity, both in components and superspace. In a superconformal framework, the deformations are associated with (composite) linear multiplets. We engineer an off-shell model that exhibits partial local supersymmetry breaking with a zero cosmological constant. This is based on the hyper-dilaton Weyl multiplet introduced in arXiv:2203.12203, coupled to the SU(1,1)/U(1) special-K\"ahler sigma model in a symplectic frame admitting a holomorphic prepotential, with one compensating and one physical vector multiplet, the latter magnetically deformed.