Lessons from the Vacuum Structure of 4d N=2 Supergravity

TL;DR

This work analyzes the vacuum structure of four-dimensional $N=2$ supergravity, focusing on backgrounds that preserve some or all supersymmetry. It develops a unified framework for fully BPS vacua, supersymmetric black holes (both asymptotically Minkowski and AdS), and the associated BPS bounds via superalgebras, including new results on black hole near-horizon algebras and a no-go theorem for static BPS AdS black holes without hypermultiplets. The thesis connects pure supergravity to string/M-theory via flux compactifications and AdS/CFT and demonstrates a holographic-like, finite charge construction that emerges from the superalgebra. It also presents a solution-generating technique via Higgsing and spontaneous symmetry breaking, enabling embedding of ungauged solutions into gauged SUGRA with nontrivial scalar profiles. The findings have implications for moduli stabilization, AdS/CFT applications, attractor flows, and the microscopic understanding of AdS black holes, including potential M-theory liftings and holographic renormalization of charges.

Abstract

This PhD thesis is devoted to the study of supersymmetry preserving background solutions of N=2 supergravity in 4 dimensions. The main contents are divided into three major parts, briefly summarized as follows. Part I deals with analysis of maximally supersymmetric configurations. Part II discusses BPS black holes with Minkowski and anti-de Sitter (AdS) asymptotics. The main topics in part III are superalgebras, BPS bounds and conserved charges for asymptotically flat or AdS spacetimes. Most of the chapters are based on previously published results with the exception of chapter 10 in part III, which is genuinely new and discusses the superalgebras of black hole configurations and their near-horizon geometries. A no-go theorem for static BPS black holes in AdS is proven in theories without hypermultiplets and the analogous situation in 5d is briefly explained.