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SUPERGRAVITY, STRING THEORY and BLACK HOLES by Nikolay P. Bobev a Dissertation Presented to the FACULTY of the USC GRADUATE SCHO

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View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Lirias SUPERGRAVITY, STRING THEORY AND BLACK HOLES by Nikolay P. Bobev A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (PHYSICS) August 2010 Copyright 2010 Nikolay P. Bobev Acknowledgments In the last four years I had the great pleasure of having Nick Warner as my Ph.D. advisor. I am grateful to Nick for all the encouragement and support during the long route that led to the writing of this thesis. Nick shaped my understanding about black holes, string theory, supergravity and many other topics in Physics and Mathematics and played an instrumental roleˆ in the research presented here. I can only hope that I was able to learn from his profound physical intuition and great technical abilities. I really cherish our innumerable discussions on topics ranging from ample divisors and rigid Calabi- Yau manifolds to French wine and Belgian beer, from gauged supergravity and Killing spinors to Doctor Who and Eddie Izzard, from black-hole microstates and wormholes to British history and American elections. Thanks also to Nick, together with Lisa, Antonia and Evelyn, for being great hosts and for the many excellent dinners and interesting conversations in their house. I would like to thank Iosif Bena for the collaboration on the research projects pre- sented in this thesis as well as for the numerous enjoyable discussions that improved my understanding of D-branes and black holes. I appreciate also his hospitality during my visits to IPhT - Saclay. The last part of this thesis is a summary of work I did in collaboration with Clement´ Ruef. Clement´ is a great guy and I would like to thank him for the endless hours we spent together pondering over factors of two and minus signs. I am grateful to Krzysztof Pilch for his willingness to correct my confusions about supergravity, group theory and many other topics in Physics and Mathematics. He also provided a healthy dose of skepticism about everything I said and had this great Eastern European attitude towards life, which reminded me of home. ii Clifford Johnson is the main reason I started the long trip from Varna to Los Angeles. He called me on the phone and said “It will be great to have you here!” and I am grateful for that. I appreciate also his encouragement, support and friendly attitude. Thanks also for the great class on D-branes! My undergraduate advisor, Radoslav Rashkov, taught me many things about Theo- retical Physics and showed me the exciting path of research in String Theory. Thanks for the great advice and support in the early days of my graduate studies. I would like to thank Nick Halmagyi, Arnab Kundu, Krzysztof Pilch and Mukund Rangamani for the enjoyable collaboration on research projects that did not make it into this thesis. It was great fun talking to them about Physics and I learned a lot along the way. Thanks also to Nick Halmagyi for the Australian accent. I would like to thank also my fellow students at the High Energy Theory Group at USC for the many conversations over a cup of coffee or a pint of beer. Tameem Albash had his office door always open for me and I am grateful for his friendship and polite attitude. The numerous conversations with Veselin Filev were always fun and I appreciate his endless energy to talk about Physics. Arnab Kundu was always ready to chat about Physics, even when what I had to say was not interesting. Min Woo Suh tested my ability to explain Physics and Mathematics many times and I thank him for his patience. Itzhak Bars, Francis Bonahon, Stephan Haas, Clifford Johnson, Krzysztof Pilch and Nick Warner kindly agreed to serve on the committees for my qualifying exam and dissertation defense and I would like to thank them for their time and for the useful feedback. Thanks also to Lisa, Mary Beth and Stephan without whom the Physics Department at USC will be a very different place. During my five years at USC I attended many classes which were instrumental in my education. Thanks to Itzhak Bars, Ko Honda, Clifford Johnson, Dennis Nemeschansky, iii Hubert Saleur, Nick Warner and Paolo Zanardi for the great lectures and for being polite enough to patiently answer my questions. In the fourth year of my Ph.D. studies I had the pleasure of spending a semester as a graduate fellow at KITP. This was an excellent scientific experience and a lot of fun. I would like to thank Joe Polchinski for making this visit possible and for his friendly attitude. Thanks also to Alex, Fiona, Javi and Mike for being great office mates. In my graduate studies I had a lot of interesting discussions about Physics, Mathe- matics and many other topics with students, postdocs and professors at various schools, workshops and conferences. Thanks to all of them for these interactions, which were a major part of my education as a physicist. In particular I would like to thank - Tameem Albash, Steve Avery, Aaron Bergman, Matt Buican, Fiona Burnell, Borun Chowdhury, Geoffrey Compere,` Jan de Boer, Sophie de Buyl, Stephane´ Detournay, Sheer El-Showk, Roberto Emparan, Veselin Filev, Sebastian´ Franco, Stefano Giusto, Murat Gunaydin,¨ Nick Halmagyi, Amihay Hanany, Veronika Hubeny, Shamit Kachru, Arnab Kundu, Sub- haneil Lahiri, Josh Lapan, Alex Levchenko, Don Marolf, Samir Mathur, Mike Mulligan, Nikita Nekrasov, Joe Polchinski, Silviu Pufu, Mukund Rangamani, Matt Roberts, Radu Roiban, Clement´ Ruef, Ashish Saxena, Sakura Schafer-Nameki,¨ Akhil Shah, Carlos Tamarit, Ketan Vyas, Chih-Wei Wang, Sho Yaida, Masahito Yamazaki and Kentaroh Yoshida. Thanks also to the Particle Theory Group at Caltech for hosting excellent seminars every Friday and for welcoming the attendance of a USC graduate student. It is a pleasure to thank Toby Jacobson and Bruna de Oliveira for being great friends during the last five years. Toby’s open-minded attitude and patience were crucial for my adaptation to life in California. He also taught me the intricacies of Californian English and the true meanings of the word “dude” and the suffix “-izzle”. Bruna showed me that there are many other interesting things in Brazil, beyond football and Bossa Nova. She also makes great cakes. iv Thanks to the Bulgarian gang at USC, Denitsa, Iskra, Marto, Ogy and Veso, for the numerous nights out and for introducing me to some important aspects of the American culture. Thanks go also to my buddies from the University of Sofia - Elica, Danail, Galin, Ivan and Stanimir. We learned a lot of Physics and Math together and enjoyed some beers in the process. I am grateful to my friends - Iliya, Konstantin, Nikolay, Radena, Stella, Vera, Yurii and Zornitsa. They helped me keep my sanity during hard times and always picked up the phone when I called. As good friends they are also always there to make fun of me when I start to take myself too seriously. Thank you for everything! My favorite football team, CSKA Sofia, performed poorly in the last five years which helped me spend more time doing Physics and facilitated the timely completion of this thesis. Thank you guys for doing this! I would like to thank my grandparents for always being there and supporting me. Thanks also to my mother-in-law, Snezhana, for providing crucial help in the final stages of the preparation of this thesis. Thanks to my sister, Dima, for the numerous excellent phone conversations in the last five years. It seems to me that the 11,000 kilometers between us brought us closer together. Words fail me to express my gratitude towards my mom, Didi, and my dad, Plamen. They taught me to value education above all else and I would not have been where I am now without their endless love, support and sacrifice. Elena is a true friend and continues to inspire me every day with her love and sense of humor. She was next to me along every step of the long journey that we started five years ago. This thesis would simply have not been possible without her love, help and v support. She introduced me to Boyan only two weeks ago and I am looking forward to the exciting path that we are about to embark upon together. During the last five years I have received financial support from various institu- tions and organizations. Thanks to the Physics and Astronomy Department at USC, the KITP-Santa Barbara and the IPhT-Saclay. My research was also supported by the John Stauffer Fellowship from USC, the Dean Joan M. Schaefer Research Scholarship, the USC Research and Travel Award and funds from the DOE under grant DE-FG03-84ER- 40168. vi Table of Contents Acknowledgments ii List of Figures x Abstract xii Introduction 1 Chapter 1: Black Holes, Supergravity and D-branes 6 1.1 Black holes . .6 1.1.1 The Reissner-Nordstrom¨ black hole . .6 1.1.2 Black-hole thermodynamics . 14 1.2 Supergravity, String Theory and D-branes . 17 1.2.1 BPS states . 18 1.2.2 Eleven-dimensional supergravity . 20 1.2.3 Type IIA and Type IIB supergravity . 23 1.2.4 Black hole entropy from string theory . 27 Chapter 2: Three-charge solutions and microstate geometries 31 2.1 Systems with microscopic horizons . 34 2.2 The three-charge system . 36 2.2.1 Supersymmetric configurations . 39 2.2.2 The BPS equations . 43 2.2.3 BMPV black hole . 46 2.2.4 Gibbons-Hawking Metrics .
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