STUDIES ON GAUGE THEORIES FROM STRING THEORY AND SCATTERING AMPLITUDE METHODS (Spine Title: Holographic Gauge Theories and Tree Level S-Matrix) (Thesis Format: Integrated-Article) by Paolo Benincasa Graduate Program in Applied Mathematics (Theoretical Physics) A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Faculty of Graduate Studies The University of Western Ontario London, Ontario, Canada ©Paolo Benincasa 2008 Library and Bibliotheque et 1*1 Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A0N4 Ottawa ON K1A0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-39242-3 Our file Notre reference ISBN: 978-0-494-39242-3 NOTICE: AVIS: The author has granted a non­ L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce, Canada de reproduire, publier, archiver, publish, archive, preserve, conserve, sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par Plntemet, prefer, telecommunication or on the Internet, distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non­ sur support microforme, papier, electronique commercial purposes, in microform, et/ou autres formats. paper, electronic and/or any other formats. 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Canada THE UNIVERSITY OF WESTERN ONTARIO FACULTY OF GRADUATE STUDIES CERTIFICATE OF EXAMINATION Supervisor Examiners Dr. Alex Buchel Dr. Mikko Karttunen Advisory committee Dr. Gerry McKeon Dr. Gerry McKeon Dr. Martin Houde Dr. Volodya Miransky Dr. Jaume Gomis The thesis by Paolo Benincasa entitled: STUDIES ON GAUGE THEORIES FROM STRING THEORY AND SCATTERING AMPLITUDES METHODS is accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy Date- Chair of the Examination Board n ABSTRACT In this thesis we investigate different aspects of gauge theories, both at strong and weak coupling, which seem hard to address using standard field theory meth­ ods. Specifically, we focus on both strongly-coupled gauge theory plasmas and the perturbative regime of General Relativity (GR) as well as arbitrary spin particles. In the first case the conjectured gauge/string correspondence is used. We extracted hydro dynamical properties of some non-conformal theories at large N and large 't Hooft coupling. For the first time the bulk viscosity for a non-conformal theory has been computed. In the models analyzed the values for the speed of sound are less than its value in conformal theories. Another interesting feature is that, turning on chemical potentials, gauge theories admitting a dual string theory still belong to the universality class defined by the ratio shear viscosity by entropy density. We also studied the implication of introducing the leading a'-correction in string the­ ory. The consistent hydrodynamical picture obtained is a test for the a'-structure of the theory. All these results hold for static plasmas. We also attempted to study plasmas as dynamical phases. Because of logarithmic singularities, the supergrav- ity approximation turns out to be inconsistent and one would need the full string theory. At weak coupling, we investigated properties of GR and interactive theories of arbitrary spin particles from an S-matrix point of view. At tree level, looking at the singularity structure of the amplitudes, n-graviton amplitudes turn out to be uniquely determined by three-graviton amplitudes. Moreover, we have formulated consistency conditions for the existence of a particular class of high spin theories admitting an S-matrix. Keywords : String Theory, Gauge/Gravity Correspondence, Thermal Field Theory, Supersymmetric Gauge Theory, Scattering Amplitudes, Classical Theories of Gravity, Gauge Symmetry. iii AUTHORSHIP This integrated-article thesis contains seven papers which have been published in five different international journals and/or have been posted on the online archive http://arxiv.org. Prof. Alex Buchel, as my current supervisor, is co-author in five of them. Chapter 6 contains a paper in collaboration with Prof. Alex Buchel and Michal Heller and Romuald Janik from Jagellonian University. Chapter 8 is the result of a collaboration with Camille Boucher-Veronneau from Waterloo University (now in Stanford) and Dr. Freddy Cachazo from Perimeter Institute for Theoretical Physics. Chapter 9 contains a paper which is a result of a collaboration with Dr. Freddy Cachazo. Approval from all parts, including co-authors as well as publishers, has been granted to include the results from the aforementioned articles within this thesis. IV // knowledge can create problems, it is not through ignorance that we can solve them. Isaac Asimov In some sort of crude sense, which no vulgarity, no humor, no overstatement can quite extinguish, the physicists have known sin; and this is a knowledge which they cannot lose. J. Robert Oppenheimer It takes so long to train a physicist to the place where he understands the nature of physical problems that he is already too old to solve them. Eugene Wigner v To those who are always with me VI ACKNOWLEDGEMENTS This thesis represents the end of another stage of my life. It is indeed simply the achievement of an intermediate step, but nevertheless it has a key role in my growing process, both as (hopefully) a researcher and as a person. It represents the end of my first experience outside my home-country. It represents the end of my path as a student. From now on it is completely up to me. For all these reasons, I would like to thank several people who played an impor­ tant role in this stage of my life. Firstly, I would like to thank my parents, to whom it was not easy to live the idea that one of their sons were in another continent - in the "America"-, and my brother Francesco for their love and their unconditional support. Well, to be completely honest, I should thank my brother also for his constant technological support in remote!! I would like to thank my advisor, Alex Buchel, who decided to accept me as his first graduate student on the basis of one single email I sent him in the fall of 2004. He guided me through the world of research, enthusiastically proposing me projects, prompting me to participate to international conferences since the very beginning of my PhD and trying to make me become an independent researcher, I enjoyed our conversations in our weekly trips to Perimeter Institute, in which I had the chance to keep learning as well as make fun about food habits and my Italy. I really hope I have made treasure of his advice. I also have to thank him for having introduced me to Perimeter Institute, where I have been part of a beautiful string theory group. Without participating to its activities, my PhD experience would not have been the same. I have benefitted very much from the interactions with its members. I am especially grateful to Freddy Cachazo, whom I have had - and I am having - the luck of collaborating with. I am grateful to him for everything he taught me and being so available for discussions. vii I also thank Fiorenzo Bastianelli, who saw me moving my very first steps in the research world, for his constant support after I left the Universita di Bologna. I am in debt with Alex, Freddy and Fiorenzo for having helped me to put some more bricks in building my future: if I can finish my PhD knowing that I will join a really good research group as postdoctoral fellow, I own it to them. I did not really expect that the outcome of my postdoctoral application would have been as great as has been. For interesting discussions about physics and nice time spent in schools and con­ ferences, it is a pleasure to thank Fernando Alday, Michele Arzano, Sujay Ashok, Roberto Balbinot, Ling Bao, Francesco Benini, Francesco Blanco, Camille Boucher- Veronneau, Stan Brodsky, Diego Chialva, Andres Collinucci, Paul Cook, Clau- dio Coriano, Olindo Corradini, Jan de Boer, Eleonora Dell'Aquila, Erik Devetak, Bianca Dittrich, Rossella Ferrandes, Valentina Giangreco, Simone Giombi, Luca Grisa, Jaume Gomis, Amihay Hanany, Michal Heller, Barbara Jacak, Niklas Jo­ hansson, Thomas Klose, Mira Kramer, Josh Lapan, Magdalena Larfors, Paola La Rocca, Xiao Liu, Pierpaolo Mastrolia, Shunji Matsuura, Paul McFadden, Gerry McKeon, Chris Miller, Volodya Miransky, Rob Myers, Suresh Nampuri, Hiroshi Ooguri, Sara Pasquetti, Filippo Passerini, Antonio Polosa, Shlomo Razamat, Slava Rychkov, Massimiliano Rinaldi, David Skinner, Julian Sonner, Simone Speziale, Andrei Starinets, Nemani Suryanarayana, Stefan Theisen, Maciej Trzetrzelewski, Mirian Tsulaia, Linda Uruchurtu-Gomez, Samuel Vazquez, David Vegh, Alessandro Vichi, Amos Yarom. A special thank is to Vic Elias who prematurely left us in 2006. I am also grateful to Claudio Coriano and the Theoretical physics group at Universita di Lecce for their hospitality during my visit and Graham Shore and Toby Wisemann for their help during my postdoctoral application process.