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Effective Actions from String and M-Theory: Compactifications on G2-Manifolds and Dark Matter in the KL Moduli Stabilization

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Effective actions from string and M-theory: compactifications on G2-manifolds and dark matter in the KL moduli stabilization scenario Dissertation zur Erlangung des Doktorgrades (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn von Thaisa Carneiro da Cunha Guio aus Vitória, ES, Brasilien Bonn, July 2018 Dieser Forschungsbericht wurde als Dissertation von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Bonn angenommen und ist auf dem Hochschulschriftenserver der ULB Bonn http://hss.ulb.uni-bonn.de/diss_online elektronisch publiziert. 1. Gutachter: Prof. Dr. Albrecht Klemm 2. Gutachter: Priv. Doz. Dr. Stefan Förste Tag der Promotion: 21.09.2018 Erscheinungsjahr: 2018 Dedicated to the loving memory of my grandmothers Aurora and Lêda, who went to a better world while I was abroad. Abstract In this thesis we study the emergence of four-dimensional effective actions from compacti- fications of higher-dimensional string/M-theory and explore some of their phenomenological implications. In order to compactify eleven-dimensional M-theory to a four-dimensional effective N = 1 supergravity action, the relevant internal spaces turn out to be G2-manifolds. Contrary to Calabi– Yau manifolds appearing in compactifications of string theory, the construction of G2-manifolds is not directly obtained via standard techniques of complex algebraic geometry. For this reason, there were up to now only a few hundred examples of them. In the first part of this thesis, we find many novel examples of G2-manifolds based on the so-called twisted connected sum construction. Furthermore, we identify a limit in which the G2-metric is approximated in terms of the metrics of the constituents of this construction, allowing for the identification of universal moduli fields in the four-dimensional effective spectrum. A final expression for a (positive semi- definite) Kähler potential in terms of these moduli is obtained, together with interesting Abelian and non-Abelian enhanced supersymmetric (N = 2 and N = 4) gauge theory sectors including, for example, the Standard Model gauge group and possible grand unification scenarios. In the second part we investigate the emergence of dark matter candidates from effective actions. Here we already start with a four-dimensional effective action motivated from F- theory/type IIB string theory on Calabi-Yau manifolds in the Kallosh–Linde (KL) moduli stabilization scenario. The non-positive vacuum in the KL scenario is uplifted by the Intriligator– Seiberg–Shih (ISS) sector, based on the free magnetic dual of N = 1 supersymmetric QCD. We analyze interactions between the KL-ISS and the Minimal Supersymmetric Standard Model (MSSM) sectors in order to investigate the dynamics after the inflationary phase, obtaining constraints from late entropy production. Finally, we obtain neutralino dark matter candidates compatible with the observed dark matter relic density from both thermal and non-thermal production. Acknowledgements First of all, I would like to thank my supervisor Albrecht Klemm for the opportunity to be a member of his research group. His friendly character provided a nice working atmosphere where we could discuss a manifold of topics on several occasions. I am profoundly grateful for his teachings on String Theory, and for his many valuable and inspiring ideas throughout these years, which I will carry along with me. I am also indebtful to my second mentor and collaborator, Hans Jockers, with whom I had many discussions that helped me progress in my research. I would like to thank Stefan Förste for being the second referee of this thesis. The opportunity to tutor in several of his lectures at the University, together with his patience and constant feedback, provided me with a valuable teaching experience, for which I am deeply grateful. I extend my thanks to Jochen Dingfelder and Matthias Lesch for also agreeing to be members of my PhD committee. I also thank Hung-Yu Yeh and Ernany Rossi Schmitz for their collaboration in parts of the work presented here, as well as Manuel Drees for discussions that significantly improved the results of the second part of this thesis. I am also thankful to the many colleagues I had throughout the years at the Bethe Center for Theoretical Physics. Many thanks to my current research group colleagues: Abhinav, Andreas, Cesar Alberto, Christoph, Fabian, Mahsa, Reza, Thorsten and Urmi. I had many interesting conversations with them during my PhD years on the most diverse topics and we shared many experiences together. In particular, I want to thank Cesar Alberto, Yeh, Iris, Jie and Paulina for their constant friendship and the many laughs we shared. Some helped me improving my Spanish and German, some are trying to make me learn Chinese. I also thank Cesar Alberto for increasing my list of books to read, and Iris for the nice football matches we played together and for her support when I had to go through knee surgery. Special thanks to the amazing friends I made in Germany: Ernany Rossi Schmitz, Felipe Padilha Leitzke, Mariana Madruga de Brito and Rachel Werneck. We shared many invaluable experiences together, finding endless meanings for everything, through the difficulties and the good times we spent together in trying to reach the same goal of completing our PhDs. I could not have stayed strong without their constant support and friendship, which I am sure will last for our whole lives. I would also like to thank my amazing friends back in Brazil, who supported me from all this distance during these years. You were always with me in my thoughts, and soon I will be there with you again. I am thankful to the Bonn-Cologne Graduate school of Physics and Astronomy for selecting i me as a member of the honors branch program, which provided me with partial financial support for some PhD years, and helpful funding to attend conferences and workshops. I am indebted to the funding program Ciências Sem Fronteiras of the brazilian federal agency CNPq, which provided me with full financial support during my PhD. I hope I will be able to return this investment in contributing to the development of science in Brazil. I am deeply thankful to my love, Gláuber Carvalho Dorsch. For his comprehension at even the most difficult times, when we worked in different places of the world in order to advance our scientific careers. For having stood by my side raising my mood at all times. For all the marvelous moments we are sharing everyday, and the many discussions regarding basically everything. I am more than certain that we are made for each other. Eu te amo demais! Last but not least I would like to thank my parents Carmem and Vicente, and my brother Matheus, for so many reasons that it would be impossible to list them all here. I am extremely grateful for the environment they provided me with, allowing me to dedicate myself entirely to my studies. I am thankful for the invaluable education I gained from them, and for their incentive to always keep following my dreams and beliefs throughout my life. Without them, nothing would have been possible. Thank you all! ii Contents Acknowledgements i 1 Introduction 1 1.1 The pillars of high energy physics and where they start to crack . .1 1.2 String theory and compactifications . .5 1.3 M-theory and G2-manifolds . .6 1.4 Dark matter in the KL moduli stabilization scenario . 11 1.5 Outline of this thesis . 13 I M-theory compactifications on G2-manifolds 15 2 G2-manifolds 19 2.1 Geometry and Topology of G2-manifolds . 20 2.1.1 The exceptional Lie group G2 and the G2-structure . 20 2.1.2 The G2-manifold . 21 2.1.3 Topology of compact G2-manifolds . 22 2.1.4 Moduli space of compact G2-manifolds . 25 2.2 Twisted connected sum G2-manifolds . 26 2.2.1 Asymptotically cylindrical Calabi–Yau threefold . 26 2.2.2 The twisted connected sum construction . 28 2.2.3 The Kovalev limit . 32 2.2.4 Cohomology of twisted connected sum G2-manifolds . 36 2.2.5 Examples of asymptotically cylindrical Calabi–Yau threefolds . 39 2.2.6 The orthogonal gluing method . 41 3 Effective action from M-theory on G2-manifolds 45 3.1 The Kaluza-Klein reduction on G2-manifolds . 45 3.2 The bosonic action . 54 3.2.1 The Kähler potential and the gauge kinetic coupling function . 57 3.3 The fermionic action . 58 3.3.1 The holomorphic superpotential . 59 3.4 M-theory on twisted connected sum G2-manifolds . 61 3.4.1 The Kähler potential: a reduced form . 61 iii 3.4.2 The four-dimensional N = 1 effective supergravity spectrum . 69 3.4.3 The final Kähler potential and its phenomenological properties . 74 4 Gauge sectors on twisted connected sum G2-manifolds 77 4.1 Abelian N = 4 gauge theory sectors . 77 4.2 N = 2 gauge theory sectors . 86 4.2.1 Phases of N = 2 Abelian gauge theory sectors . 88 4.2.2 Phases of N = 2 non-Abelian gauge theory sectors . 93 4.2.3 Examples of G2-manifolds with N = 2 gauge theory sectors . 97 4.2.4 Transitions among twisted connected sum G2-manifolds . 104 II Dark matter in the KL moduli stabilization scenario 107 5 The KL-ISS scenario 111 5.1 The Kallosh–Linde (KL) moduli stabilization scenario . 111 5.2 The Intriligator–Seiberg–Shih (ISS) sector . 114 5.3 The MSSM and the inflationary sectors . 115 5.4 F-term uplifting in the KL-ISS scenario . 116 5.5 Properties of the KL-ISS-MSSM setup . 118 5.5.1 Masses . 118 5.5.2 Decay rates . 123 6 Dark matter in the KL-ISS-MSSM scenario 127 6.1 Post-inflation dynamics .
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