The linear multiplet and ectoplasm

TL;DR

This paper develops a superform formulation for the linear multiplet in 4D N=2 supergravity, introduces a new supersymmetric action with a deformed multiplet, and explores its relation to gauged central charge and vector-tensor multiplets.

Contribution

It provides a novel superform approach to the linear multiplet and constructs a new locally supersymmetric action involving a deformed multiplet with gauged central charge.

Findings

Superform formulation for the linear multiplet in supergravity.

New supersymmetric action using a deformed linear multiplet.

Connection to gauged central charge and vector-tensor multiplet variants.

Abstract

In the framework of the superconformal tensor calculus for 4D N=2 supergravity, locally supersymmetric actions are often constructed using the linear multiplet. We provide a superform formulation for the linear multiplet and derive the corresponding action functional using the ectoplasm method (also known as the superform approach to the construction of supersymmetric invariants). We propose a new locally supersymmetric action which makes use of a deformed linear multiplet. The novel feature of this multiplet is that it corresponds to the case of a gauged central charge using a one-form potential not annihilated by the central charge (unlike the standard N=2 vector multiplet). Such a gauge one-form can be chosen to describe a variant nonlinear vector-tensor multiplet. As a byproduct of our construction, we also find a variant realization of the tensor multiplet in supergravity where one of the auxiliaries is replaced by the field strength of a gauge three-form.