Field theory in 4D N=2 conformally flat superspace

TL;DR

This paper explores the structure of field theories in four-dimensional N=2 conformally flat superspaces, focusing on AdS superspace, revealing a unique vector multiplet that encodes the supergeometry and aids in constructing supersymmetric actions.

Contribution

It introduces a unique vector multiplet associated with N=2 AdS supergeometry, which encodes all geometric information and serves as a building block for supersymmetric actions in conformally flat superspaces.

Findings

The vector multiplet W_0 is constant and intrinsic to N=2 AdS supergeometry.

W_0 encodes all information about the supergeometry in a conformally flat frame.

Explicit N=2 to N=1 superspace reduction is performed with examples.

Abstract

Building on the superspace formulation for four-dimensional N=2 matter-coupled supergravity developed in arXiv:0805.4683, we elaborate upon a general setting for field theory in N=2 conformally flat superspaces, and concentrate specifically on the case of anti-de Sitter (AdS) superspace. We demonstrate, in particular, that associated with the N=2 AdS supergeometry is a unique vector multiplet such that the corresponding covariantly chiral field strength W_0 is constant, W_0=1. This multiplet proves to be intrinsic in the sense that it encodes all the information about the N=2 AdS supergeometry in a conformally flat frame. Moreover, it emerges as a building block in the construction of various supersymmetric actions. Such a vector multiplet, which can be identified with one of the two compensators of N=2 supergravity, also naturally occurs for arbitrary conformally flat superspaces. An explicit superspace reduction N=2 to N=1 is performed for the action principle in general conformally flat N=2 backgrounds, and examples of such reduction are given.