Partition Functions For Supersymmetric Black Holes

AUP-Manschot:AUP/Voorbij 22-09-2008 11:02 Pagina 1 Faculty of Science This dissertation presents recent discoveries on partition functions for four-dimensional supersymmetric black holes. These partition functions are important tools to explain the entropy of black holes from a microscopic point of view within string theory and M-theory. The results are applied to two central research topics in modern theoretical physics, namely (1) the correspondence between the physics (including gravity) within an Anti-de Sitter space and conformal field theory, and (2) the relation between black holes and topological strings. 9 789056 295400 Jan Manschot Jan Manschot (1980) studied Applied Physics at Delft University of Technology. In 2004, he started his Ph.D. research at the Institute for Theoretical Physics of the University of Amsterdam. Partition Functions for Supersymmetric Black Holes UvA Dissertation Partition Functions for Supersymmetric Black Holes jan manschot Partition Functions for Supersymmetric Black Holes The research, which is published in this book, has been performed at the Institute for Theoretical Physics of the University of Amsterdam and has been financially supported by the Foundation of Fundamental Research on Matter (FOM). It has been carried out in the Dutch Research School of Theoretical Physics. Cover design: Ren´e Staelenberg, Amsterdam ISBN 978 90 5629 540 0 NUR 910 c Jan Manschot/Vossiuspers UvA - Amsterdam University Press, 2008 All rights reserved. Without limiting the rights under copyright reserved above, no part of this book may be reproduced, stored in or introduced into a retrieval system, or transmitted, in any form or by any means (electronic, mechanical, photocopying, recording or otherwise) without the written permission of both the copyright owner and the author of the book. Partition Functions for Supersymmetric Black Holes ACADEMISCH PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Universiteit van Amsterdam op gezag van de Rector Magnificus Prof. dr. D. C. van den Boom ten overstaan van een door het college voor promoties ingestelde commissie, in het openbaar te verdedigen in de Agnietenkapel op donderdag 18 december 2008, te 12:00 uur door Jan Manschot geboren te Alphen aan den Rijn Promotie commissie: Promotor: Prof. dr. E. P. Verlinde Overige leden: Prof. dr. J. de Boer Prof. dr. R. H. Dijkgraaf Prof. dr. G. B. M. van der Geer Prof. dr. G. W. Moore Dr. K. Skenderis Faculteit der Natuurwetenschappen, Wiskunde en Informatica PUBLICATIONS This thesis is based on the following publications: J. de Boer, M. C. N. Cheng, R. H. Dijkgraaf, J. Manschot, E. P. Verlinde, A Farey Tail for Attractor Black Holes, JHEP 11 (2006) 024, arXiv:hep-th/0608059. J. Manschot, AdS3 Partition Functions Reconstructed, JHEP 10 (2007) 103, arXiv:0707.1159 [hep-th]. J. Manschot, G. W. Moore, A Modern Farey Tail, arXiv:0712.0573 [hep-th]. J. Manschot, On the Space of Elliptic Genera, arXiv:0805.4333 [hep-th]. CONTENTS 1. Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Motivations for Black Hole Partition Functions . . . . . . . . . 2.1 Four-dimensional black holes . . . . . . . . . . . . . . . . 2.1.1 Reissner-Nordstr¨om black holes . . . . . . . . . . . 2.1.2 Black holes in N = 2 supergravity . . . . . . . . . 2.1.3 A black hole partition function and a Legendre transformation . . . . . . . . . . . . . . . . . . . . . . . 2.2 The AdS3 /CFT2 correspondence . . . . . . . . . . . . . . 2.2.1 The correspondence . . . . . . . . . . . . . . . . . 2.2.2 Gravity in asymptotic AdS3 . . . . . . . . . . . . . 9 10 10 13 20 26 27 31 <