Electric and magnetic charges in N=2 conformal supergravity theories

TL;DR

This work develops a comprehensive embedding-tensor framework for gauged N=2 conformal supergravity in four dimensions, unifying electric and magnetic charges within a duality-covariant (symplectic) formulation. It constructs general Lagrangians for vector and hypermultiplets, introduces a tensor hierarchy to accommodate magnetic gaugings, and derives the complete gauged superconformal algebra including mass terms and a g^2 scalar potential. The embedding-tensor approach clarifies locality constraints, closure relations, and the role of moment maps, providing a versatile toolkit to study deformations of matter-coupled N=2 theories and to classify supersymmetric solutions in maximally symmetric spaces and in AdS$_2 imes$S$^2$ geometries. The paper ultimately shows that admissible supersymmetric configurations in AdS$_2 imes$S$^2$ fall into two realized classes (fully supersymmetric or four supercharges), with implications for black hole horizons and supersymmetry enhancement at the horizon.

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.