Electric and magnetic charges in N=2 conformal supergravity theories

TL;DR

This paper develops a comprehensive framework for N=2 conformal supergravity theories with electric and magnetic charges, analyzing gauge interactions, scalar potentials, and classifying supersymmetric solutions in specific space-times.

Contribution

It introduces a general construction for gauge charges in N=2 supergravity, including duality covariance and a classification of supersymmetric solutions in AdS2×S2.

Findings

Scalar potential quadratic in embedding tensor

Covariance under electric/magnetic duality

Classification of solutions with 4 or 8 supersymmetries

Abstract

General Lagrangians are constructed for N=2 conformal supergravity theories in four space-time dimensions involving gauge groups with abelian and/or non-abelian electric and magnetic charges. The charges are encoded in the gauge group embedding tensor. The scalar potential induced by the gauge interactions is quadratic in this tensor, and, when the embedding tensor is treated as a spurionic quantity, it is formally covariant with respect to electric/magnetic duality. This work establishes a general framework for studying any deformation induced by gauge interactions of matter-coupled N=2 supergravity theories. As an application, full and residual supersymmetry realizations in maximally symmetric space-times are reviewed. Furthermore, a general classification is presented of supersymmetric solutions in $\mathrm{AdS}_2\times S^2$ space-times. As it turns out, these solutions allow either eight or four supersymmetries. With four supersymmetries, the spinorial parameters are Killing spinors of $\mathrm{AdS}_2$ that are constant on $S^2$, so that they carry no spin, while the bosonic background is rotationally invariant.