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Renata Kallosh Emanuele Orazi Editors Theoretical Perspective In Springer Proceedings in Physics 176 Renata Kallosh Emanuele Orazi Editors Theoretical Frontiers in Black Holes and Cosmology Theoretical Perspective in High Energy Physics Springer Proceedings in Physics Volume 176 The series Springer Proceedings in Physics, founded in 1984, is devoted to timely reports of state-of-the-art developments in physics and related sciences. Typically based on material presented at conferences, workshops and similar scientific meetings, volumes published in this series will constitute a comprehensive up-to-date source of reference on a field or subfield of relevance in contemporary physics. Proposals must include the following: – name, place and date of the scientific meeting – a link to the committees (local organization, international advisors etc.) – scientific description of the meeting – list of invited/plenary speakers – an estimate of the planned proceedings book parameters (number of pages/ articles, requested number of bulk copies, submission deadline). More information about this series at http://www.springer.com/series/361 Renata Kallosh • Emanuele Orazi Editors Theoretical Frontiers in Black Holes and Cosmology Theoretical Perspective in High Energy Physics 123 Editors Renata Kallosh Emanuele Orazi Department of Physics Escola de Ciências e Tecnologia Stanford University Universidade Federal Rio Grande do Norte Stanford, CA Natal, RN USA Brazil ISSN 0930-8989 ISSN 1867-4941 (electronic) Springer Proceedings in Physics ISBN 978-3-319-31351-1 ISBN 978-3-319-31352-8 (eBook) DOI 10.1007/978-3-319-31352-8 Library of Congress Control Number: 2016937523 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland Preface This volume aims at providing a pedagogical review on recent developments and applications of black hole physics in the context of high energy physics and cos- mology. The contributions are based on lectures delivered at the school “Theoretical Frontiers in Black Holes and Cosmology”, held at the “International Institute of Physics” (IIP) in Natal, Brazil, in June 2015. The lectures give a panoramic view of mainstream research lines sharing black hole solutions to gravity and supergravity as common denominator. Starting with accessible and introduc- tory concepts, the newcomer to the field will be brought to a level suitable to face cutting-edge research in the various topics considered in this book. The only prerequisite for the reader is a working knowledge in field theory and group theory, and the knowledge of general relativity and supersymmetry is desirable. The primary audience is intended to be postgraduate students but the well-established techniques presented in this volume forms a useful review for any scientist working in the field. The selection of authors has been based on worldwide recognized contributions on geometric approaches to fundamental problems in the field of black hole physics. The book is organized as follows: Chapter “Three Lectures on the FGK Formalism and Beyond” introduces the key role of dualities and the attractor mechanism in the context of singular solutions in ungauged supergravities. These concepts are further developed in Chap. “Introductory Lectures on Extended Supergravities and Gaugings”, which is a review of the present methods to build up a gauged supergravity. A basic knowledge on how to gauge a supergravity is the necessary ingredient for Chap. “Supersymmetric Black Holes and Attractors in Gauged Supergravity” that deals with the construction of black hole solutions in a gauged supergravity. The relevance of these solutions is due to applications to gauge/gravity duality, where black hole backgrounds in the bulk are used to model finite temperature condensed matter systems on the boundary. In this framework, the asymptotical AdS space, generated by the gauging procedure, provides the right symmetries to describe a conformal system on the boundary. These first three contributions are intended to be a primer for the community of scientists working in v vi Preface the field of gauge/gravity duality that want to embed more complicated bulk backgrounds in the holographic settings. In Chap. “Lectures on Holographic Renormalization”, we selected the holographic renormalization among the many topics in gauge/gravity duality, due to the strong overlapping with techniques used to find the scalar flows for black holes backgrounds in supergravity. Chapter “Nonsingular Black Holes in Palatini Extensions of General Relativity” introduces the reader to a different formulation of gravity based on metric-affine spaces. This approach allows to remove the singularity of general relativity giving rise to a wormhole structure. Finally, Chap. “Inflation: Observations and Attractors” is an introduction to inflation both from theoretical and experimental points of view, aimed at describing the role of cosmological attractors for inflationary model building. We acknowledge the staff at the IIP for the support in organizing the school “Theoretical Frontiers in Black Holes and Cosmology” where these lectures have been delivered. Stanford Renata Kallosh Natal Emanuele Orazi Contents Three Lectures on the FGK Formalism and Beyond............... 1 Tomás Ortín and Pedro F. Ramírez Introductory Lectures on Extended Supergravities and Gaugings .............................................. 41 Antonio Gallerati and Mario Trigiante Supersymmetric Black Holes and Attractors in Gauged Supergravity............................................ 111 Dietmar Klemm Lectures on Holographic Renormalization ...................... 131 Ioannis Papadimitriou Nonsingular Black Holes in Palatini Extensions of General Relativity .............................................. 183 Gonzalo J. Olmo Inflation: Observations and Attractors......................... 221 Diederik Roest and Marco Scalisi Index ................................................. 251 vii Contributors Pedro F. Ramírez Instituto de Física Teórica UAM/CSIC C/ Nicolás Cabrera, Madrid, Spain Antonio Gallerati Department DISAT, Politecnico di Torino, Torino, Italy Dietmar Klemm Dipartimento di Fisica, Università di Milano and INFN, Sezione di Milano, Milano, Italy Gonzalo J. Olmo Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia—CSIC, Paterna, Spain; Universidad de Valencia, Valencia, Spain; Departamento de Física, Universidade Federal da Paraíba, João Pessoa, Paraíba, Brazil Tomás Ortín Instituto de Física Teórica UAM/CSIC C/ Nicolás Cabrera, Madrid, Spain Ioannis Papadimitriou SISSA and INFN—Sezione di Trieste, Trieste, Italy Diederik Roest Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Groningen, The Netherlands Marco Scalisi Van Swinderen Institute for Particle Physics and Gravity, University of Groningen, Groningen, The Netherlands Mario Trigiante Department DISAT, Politecnico di Torino, Torino, Italy ix Three Lectures on the FGK Formalism and Beyond Tomás Ortín and Pedro F. Ramírez Abstract We review the formalism proposed by Ferrara, Gibbons and Kallosh to study charged, static, spherically symmetric black-hole solutions of d = 4 supergravity-like theories and its extension to objects of higher worldvolume dimen- sions in higher spacetime dimensions and the so-called H-FGK formalism based on variables transforming linearly under duality in the effective action. We also review applications of these formalisms to 4- and 5-dimensional supergravity theories. 1 The FGK Formalism for d = 4 Black Holes Many results in black-hole physics1 have been derived from the study of families of solutions, that is, solutions whose fields depend on a number of independent physical parameters (mass, electric and magnetic charges, angular momentum and moduli). Obtaining these families of solutions requires, typically, a great deal of effort. The FGK formalism [2] that we are going to review in this lecture dramatically simplifies this task for the static case in supergravity-like field theories. But it does much more than that, since it allows us to derive generic results about entire families of solutions without having to find them explicitly. One of these results is the general form of the celebrated attractor mechanism [3–6] that controls the behaviour of scalar fields in the near-horizon limit for extremal black holes and leads to the conclusion that their
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