ADVENTURES IN HETEROTIC STRING PHENOMENOLOGY DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By George Benjamin Dundee, B.S., M.S. Graduate Program in Physics The Ohio State University 2010 Dissertation Committee: Stuart A. Raby, Advisor Samir D. Mathur John F. Beacom Richard Kass c Copyright by George Benjamin Dundee 2010 ABSTRACT In this Dissertation, we consider three topics in the study of effective field theories derived from orbifold compactifications of the heterotic string. In Chapter 2 we provide a primer for those interested in building models based on orbifold compactifications of the heterotic string. In Chapter 3, we analyze gauge coupling unification in the context of heterotic strings on anisotropic orbifolds. This construction is very much analogous to effective five dimen- sional orbifold GUT field theories. Our analysis assumes three fundamental scales, the string scale, MS, a compactification scale, MC, and a mass scale for some of the vector-like exotics, MEX; the other exotics are assumed to get mass at MS. In the particular models an- alyzed, we show that gauge coupling unification is not possible with MEX = MC and in fact we require M M 3 1016 GeV. We find that about 10% of the parameter space has EX C ∼ × a proton lifetime (from dimension six gauge exchange) 1033 yr τ(p π0e+) 1036 yr, . ! . which is potentially observable by the next generation of proton decay experiments. 80% of the parameter space gives proton lifetimes below Super-K bounds. In Chapter 4, we examine the relationship between the string coupling constant, gSTRING, and the grand unified gauge coupling constant, αGUT, in the models of Chapter 3. We find that the requirement that the theory be perturbative provides a non-trivial constraint on these models. Interestingly, there is a correlation between the proton decay rate (due to dimension six operators) and the string coupling constant in this class of models. Finally, we make some comments concerning the extension of these models to the six (and higher) dimensional case. In Chapter 5, we discuss the issues of supersymmetry breaking and moduli stabiliza- tion within the context of E8 E8 heterotic orbifold constructions and, in particular, we fo- ⊗ cus on the class of “mini-landscape” models. These theories contain a non-Abelian hidden gauge sector which generates a non-perturbative superpotential leading to supersymme- try breaking and moduli stabilization. We demonstrate this effect in a simple model which contains many of the features of the more general construction. In addition, we argue that ii once supersymmetry is broken in a restricted sector of the theory, then all moduli are sta- bilized by supergravity effects. Finally, we obtain the low energy superparticle spectrum resulting from this simple model. iii Let him who seeks not cease seeking until he finds; and when he finds he shall be troubled; and having been troubled he shall marvel. The Gospel of Thomas I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. Isaac Newton iv ACKNOWLEDGMENTS Whatever successes I have had in life are due, in no small part, to those around me. The first acknowledgment is ostensibly reserved for one’s advisor, and I can not recognize mine enough. I am eternally grateful to Stuart Raby for his patience in passing on his expertise—I will hold his advice closely: “Don’t talk, just think!”. Other faculty at Ohio State have been instrumental in my development as well: I would like to specifically thank John Beacom (for teaching me how to read papers), and Samir Mathur (for teaching me to break difficult concepts down to their rudiments), who have helped me develop insight at two very opposite ends of physics. And I must also acknowledge my former advisor, Gerald Cleaver, for his support and encouragement when I decided to leave Baylor with a Master’s degree. I have had the pleasure to collaborate with Alex Westphal (who knows about ev- erything from supercavitation to the iPad) and Akin Wingerter. Though we have never worked together, I would like to thank Konstantin Bobkov for happy hours on Fridays, and for trying to teach me inflation. I would also like to thank Steve Avery, Tassos Taliotis, Yogesh Shrivastava (whose last name, appropriately enough, means “the guru”), Borun Chowdhury and Jeremy Michel- son for numerous discussions about string theory, and physics in general—from fuzzballs to nuclear physics, from Dirac brackets to superconformal symmetry, I could always count on someone to answer my questions. A special place in this section is also reserved for Matt Kistler and Hasan Yuksel,¨ who taught me to think outside of the theoretical physics box—I will miss our meetings, talking about scale invariant animals (“unimals”), social behavior of monkeys, mean bicep size of South Indians and the subtleties of ant communities. My other colleagues at Ohio State have helped me understand everything from graph- ene to microlensing: Sheldon Bailey, Jim Davis, Kevin Driver, Mike Fellinger, Dave Gohlke, Rob Guidry, Alex Mooney, James Stapleton, Jeff Stevens, Rakesh Tiwari, Greg Viera and Julia Young for evenings at the Scholar and the Library, summer softball, and barbecues at Greg’s place. At Stanford University, I had the pleasure to sit in lectures by Savas Di- mopoulous (who taught me that truly understanding something meant that one could v write down the answer without having to do any calculation) and Eva Silverstein. I con- sider myself fortunate to know Nathaniel Craig, Dan Greene, Kassa Haileyesus, Dan Har- low, Bart Horn, Eder Izaguirre, Jon Maltz, Siavosh Rezvan Behbahani, Tomas Rube, Dusan Simic and Daniele Spier Moreira Alves. I am lucky to count Josh Friess, Nadir Jevanjee and Amanda Weltman as friends. I would like to especially thank Josh for advice regarding my graduate school applications, and for advice about careers outside of academia. On a more personal level, I’d like to thank Bryanne Bornstein (for making the hard times easier to live through), and her parents (Dr. and Mrs. Bornstein) for always support- ing me. During my time at Ohio State, I have had the pleasure to speak many times with Pro- fessor Emeritus Walter Wada, who passed away shortly before I began preparing this Dis- sertation. Professor Wada’s love of physics never dissipated, and even in the last weeks of his life he was trying to convince me that right-handed neutrinos were viable dark matter candidates. I am sorry that he will not be in attendance at my Defense, and I regret that he will never see this work completed, but I do feel privileged to have known him. Most importantly, I must acknowledge the role of my parents and my grandmother in my education. It is only by their support that I am here today, and everything that I have accomplished has only been with their love and support. vi VITA Aug 26, 1979 . Born—Galveston, Texas May, 2002 . B.S., Chemistry, Baylor University, Waco, Texas Sept 2004 - Sept 2007 . Texas Space Grant Consortium Graduate Fellow Dec, 2006 . M.S., Physics, Baylor University, Waco, Texas Sept 2006 - present . Graduate Research, Dept. of Physics, The Ohio State University, Columbus, Ohio Publications K. Busch, O. Soyemi, D. Rabbe, K. Humphrey, B. Dundee, and M. Busch, “Wavelength Calibration of a Dispersive Near-Infrared Spectrometer Using Trichloromethane as a Cali- bration Standard,” Appl. Spect.54 9 (2000). O. Soyemi, D. Rabbe, B. Dundee, M. Busch, and K. Busch “Design of a Modular, Dispersive Spectrometer for Fundamental Studies in NIR Spectroscopy,” Spect.16 12 (2001). B. Dundee, J. Perkins and G. Cleaver, “Observable / hidden broken symmetry for sym- metric boundary conditions,” Int. J. Mod.Phys.A21, 3367 (2006), hep-ph/0506183. J. Perkins et al., “Stringent Phenomenological Investigation into Heterotic String Optical Unification,” Phys. Rev. D75, 026007 (2007) hep-ph/0510141. B. Dundee and G. B. Cleaver, “Randall-Sundrum and flipped SU(5),” Int. J. Mod. Phys. A 23, 2915 (2008) hep-ph/0609129. B. Dundee, S. Raby, and A. Wingerter, “Reconciling Grand Unification with Strings by Anisotropic Compactifications,” Phys. Rev. D 78 066006 (2008) , 0805.4186 vii B. Dundee, S. Raby, and A. Wingerter, “Addendum to “reconciling grand unification with strings by anisotropic compactifications”,” Phys. Rev. D 79 047901 (2009), 0811.4026. B. Dundee and S. Raby, “On the string coupling in a class of stringy orbifold GUTs,” Sub- mitted to Phys. Lett. B 0808.0992. B. Dundee, S. Raby, and A. Westphal, “Moduli stabilization and SUSY breaking in heterotic orbifold string models,” Submitted to Phys. Rev. D 1002.1081. Fields of Study Major Field: Physics Studies in Heterotic String Phenomenology: Stuart A. Raby viii Contents Page Abstract . ii Dedication . iv Acknowledgments . .v Vita ............................................... vii List of Tables ......................................... xii List of Figures ......................................... xiii Chapters 1 Introduction 1 1.1 The Standard Model and the Effective Field Theory Paradigm . 1 1.1.1 Fermi Theory: An Example . 3 1.2 Supersymmetry: A First Step . 7 1.3 Unification . 11 1.4 String Theory as a Playground . 15 1.5 Outline with an Emphasis on Original Work . 17 2 Orbifold Compactifications of the Heterotic String: A How-To Guide 20 2.1 The Heterotic String . 20 2.1.1 The Right-moving Sector . 21 2.1.2 The Left-moving Sector . 23 2.1.3 The Massless Spectrum . 24 2.1.4 Toroidal Compactification . 25 2.2 General Aspects of Orbifold Compactification .