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Supersymmetry Breaking and Its Mediation in String Theory and Particle Physics

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Supersymmetry Breaking and Its Mediation in String Theory and Particle Physics Supersymmetry Breaking and Its Mediation in String Theory and Particle Physics Matthew A. Buican A Dissertation Presented to the Faculty of Princeton University in Candidacy for the Degree of Doctor of Philosophy Recommended for Acceptance by the Department of Physics September 2009 Advisor: Herman L. Verlinde c Copyright 2009 Advisor: Herman L. Verlinde by Matthew A. Buican. All rights reserved. Abstract In this thesis, we study spontaneous supersymmetry (SUSY) breaking and its mediation from various perspectives. We begin by motivating SUSY from both phenomenological and more theoretical points of view. After undertaking a brief review of the structure and history of SUSY, we move on to study gauge-mediated SUSY breaking. We further develop a general formalism for describing the soft parameters generated in theories of gauge mediation. Using this formalism we give a general proof of the finiteness of the soft parameters. Then, specializing to weakly coupled models, we shed new light on the UV sensitivity of the soft masses. Finally, we prove that the parameter space described by our formalism is physical and realizable in calculable, weakly coupled models. This result opens up the possibility of completely new soft spectra not typically associated with gauge mediation. Next, we make contact with string theory and realize a supersymmetric extension of the Standard Model as the low energy theory of a D3 brane probing a del Pezzo singularity in a gravitational decoupling limit we describe. More importantly, we formulate new topological conditions under which the abelian gauge bosons of the D3-brane theory are rendered massive upon UV completing the singularity into a compact manifold. Shifting our focus to SUSY breaking in hidden sectors, we analyze how to generate metastable SUSY breaking quantum field theories in string theory. We give a simple set of geometrical conditions for understanding the resulting gauge theory. In the last part of the thesis, we will introduce a novel string theoretical scheme for mediating SUSY breaking using D-brane instantons. iii Acknowledgements There are far too many people to thank. During my time in Princeton, I have learned a lot of physics from discussions with Sebastian Franco, Josh Friess, Zohar Komargodski, Dmitry Malyshev, Patrick Meade, Giorgios Michalogiorgakis, Gil Paz, David Shih, Brian Wecht, and Martijn Wijnholt among others. But I would especially like to thank Herman Verlinde, my advisor, and Nati Seiberg for inspiring me with their completely unique spirits and insights into physics as well as for generously giving me their time and wonderful advice when needed. Much of the work in this thesis is based on collaborations with various subsets of these remarkable physicists. The work in Chapter 2 is in collaboration with Patrick, David, and Nati; in Chapter 3, with Dmitry, Herman, Martijn, and David Morrison; in Chapter 4, again with Dmitry and Herman; and in Chapter 5, with Sebastian. There is also more work started and yet to be finished, which I have not been able to include in this thesis, a collaboration for which I am equally grateful. My life at Princeton would not have been nearly as much fun without the friendship of these people and the presence of many others like Mike Sekora, Aric Shao, Diego Hofman, Sidhartha Goyal, Fiona Burnell, Arvind Murugan, and Marcus Bena. Finally, there are some people whom I can never thank enough. Those are my parents, but especially my mother for her complete and total love and dedication and for her un- conditional support in all of my endeavors. I also cannot forget to mention Bew—my close friend, companion, partner in adventure, and confidant through these last three years. iv Contents Abstract iii Acknowledgements iv Contents v List of Figures ix List of Tables xiii 1 Introduction 1 1.0.1 Supersymmetry.............................. 5 1.0.2 Supersymmetryandparticlephysics . 9 1.0.3 Supersymmetrybreaking .. .. .. .. .. .. .. 10 1.0.4 Mediation and soft parameters . 12 1.0.5 Supersymmetric particle physics and string theory . 14 2 General Aspects of Gauge Mediation 19 2.1 Introduction ................................... 20 2.2 General Gauge Mediation: A New and Improved Formulation . 24 2.2.1 Review and reformulation . 24 2.2.2 Generalization to the MSSM . 28 2.3 SensitivitytoUVphysics ............................ 29 v 2.3.1 Generalremarks ............................. 29 2.3.2 Example.................................. 31 2.4 Covering the General Gauge Mediation Parameter Space . 34 2.4.1 Thegeneralsetup ............................ 34 2.4.2 Covering the GGM parameter space of a toy U(1) visible sector . 36 2.4.3 Covering the MSSM GGM parameter space . 38 2.5 General results on the effective supertrace . 40 2.5.1 Integrating out massive chiral matter . 41 2.5.2 Integrating out massive vector superfields . 42 2.6 General results on multiple messenger models . 44 3 Towards the SSM in String Theory 46 3.1 Introduction ................................... 47 3.2 GeneralStrategy................................. 48 3.2.1 D-branesataCYsingularity . 49 3.2.2 SymmetrybreakingtowardstheSSM . 52 3.2.3 Summary ................................. 53 3.3 U(1)MassesviaRR-couplings . 54 3.3.1 The U(1)hypermultiplet ........................ 54 3.3.2 Somenotation .............................. 55 3.3.3 Braneaction ............................... 56 3.3.4 Some local and global considerations . 60 3.3.5 Bulkaction ................................ 62 3.3.6 Couplingbraneandbulk .. .. .. .. .. .. .. 64 3.4 SM-like Gauge Theory from a dP8 Singularity ................ 67 3.4.1 AStandardModelD3-brane . 67 3.4.2 Identification of hypercharge . 71 3.5 Constructing the Calabi–Yau Threefold . 73 3.5.1 Local Picard group of a CY singularity . 75 vi 3.5.2 Construction of the CY threefold . 77 3.6 ConclusionandOutlook............................. 82 3.6.1 U(1) Breaking via D-instantons . 83 3.6.2 Eliminating extra Higgses . 84 4 Metastable SUSY Breaking in String Theory 86 4.1 Introduction.................................... 87 2 4.2 Deformed C /Z2 ................................. 91 4.3 ISSfromtheSuspendedPinchPointsingularity. 93 4.3.1 D-branes at a deformed SPP singularity . 95 4.3.2 DynamicalSUSYbreaking . .. .. .. .. .. .. 97 4.3.3 SUSYrestoration............................. 99 4.4 TypeIIAdualoftheSPPsingularity. 104 4.5 F-termviaaDeformedModuliSpace. 106 4.6 Concludingremarks ............................... 112 4.7 ISSquiverviaanRGcascade. .. .. .. .. .. .. .. .. 113 5 SUSY Breaking Mediation by D-brane Instantons 115 5.1 Introduction.................................... 116 5.2 Generalidea.................................... 118 5.2.1 Coupling visible and hidden sectors via D-brane instantons . 118 5.2.2 Instantonmediation . 125 5.2.3 Possiblesoftterms ............................ 126 5.2.4 Possible hidden sectors and mediation mechanisms . 128 5.2.5 Relative dominance of mediation mechanisms . 129 5.3 Toroidalorientifolds .. .. .. .. .. .. .. .. .. 131 5.3.1 E3-braneinstantons . 134 5.3.2 The ZZ3 orientifold............................ 138 5.4 Examples ..................................... 141 vii 5.4.1 Dynamical SUSY breaking hidden sector . 141 5.4.2 Polonyi hidden sector . 144 5.5 Phenomenology and instanton orientation . 150 5.5.1 A broader definition of instanton orientation . 153 5.6 Furtherpossibilities ............................... 155 5.7 Conclusions .................................... 158 6 Conclusions 159 References 162 viii List of Figures 3.1 The MSSM-like quiver gauge theory obtained in [23]. Each line represents three generations of bi-fundamentals. In the text below we will identify the geometric condition that isolates the U(1)Y hypercharge as the only surviving massless U(1)gaugesymmetry. ......................... 70 3.2 Our proposed D3-brane realization of the MSSM involves a dP8 singularity embedded inside a CY manifold, such that two of its 2-cycles, α1 and α2, develop an A2 singularity which forms part of a curve of A2 singularities on the CY, and all remaining 2-cycles except α4 are non-trivial within the full CY. ........................................ 73 3.3 Starting point of our construction of a CY threefold with the desired topology. The curves fi and gi are fibers in the two rulings on S1............ 78 3.4 The CY threefold after flopping the curves C45,C6,C7 and C8. The curves f , g , C , C , C , and C are all ( 1)-curves on S ............. 79 45 45 45 6 7 8 − 5 3.5 The CY threefold after flopping C1. The curves f1, g1, and C1 are additional ( 1)-curves on S ................................. 79 − 6 3.6 The CY threefold after flopping C . The curve C has become a ( 2)-curve, 2 1 − and C is a ( 1)-curve on S ........................... 80 2 − 7 3.7 The CY threefold after flopping C . The curves C has become a ( 2)-curve, 3 2 − C remains a ( 2)-curve, and C is a ( 1)-curve on S . ........... 80 1 − 3 − 8 3.8 The final configuration: a del Pezzo 8 surface with an A2 singularity, embed- ded into a Calabi–Yau such that two of its exceptional curves are homologous. 81 ix 4.1 Quiver gauge theory for N D3-branes at a suspended pinch point singularity. 96 4.2 A particular combination of fractional branes on the SPP singularity and the corresponding quiver gauge theory that reproduce the ISS model. The cycle α1 is a non-isolated two-cycle of the deformed A1 singularity inside the SPP. The cycles α2 and α3 denote the isolated two-cycles on the two conifolds that remain after the deformation of the A1 singularity. The cycles satisfy α1 + α2 + α3 = 0. The
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