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Life at the Interface of Particle Physics and String Theory∗

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Life at the Interface of Particle Physics and String Theory∗ NIKHEF/2013-010 Life at the Interface of Particle Physics and String Theory∗ A N Schellekens Nikhef, 1098XG Amsterdam (The Netherlands) IMAPP, 6500 GL Nijmegen (The Netherlands) IFF-CSIC, 28006 Madrid (Spain) If the results of the first LHC run are not betraying us, many decades of particle physics are culminating in a complete and consistent theory for all non-gravitational physics: the Standard Model. But despite this monumental achievement there is a clear sense of disappointment: many questions remain unanswered. Remarkably, most unanswered questions could just be environmental, and disturbingly (to some) the existence of life may depend on that environment. Meanwhile there has been increasing evidence that the seemingly ideal candidate for answering these questions, String Theory, gives an answer few people initially expected: a huge \landscape" of possibilities, that can be realized in a multiverse and populated by eternal inflation. At the interface of \bottom- up" and \top-down" physics, a discussion of anthropic arguments becomes unavoidable. We review developments in this area, focusing especially on the last decade. CONTENTS 6. Free Field Theory Constructions 35 7. Early attempts at vacuum counting. 36 I. Introduction2 8. Meromorphic CFTs. 36 9. Gepner Models. 37 II. The Standard Model5 10. New Directions in Heterotic strings 38 11. Orientifolds and Intersecting Branes 39 III. Anthropic Landscapes 10 12. Decoupling Limits 41 A. What Can Be Varied? 11 G. Non-supersymmetric strings 42 B. The Anthropocentric Trap 12 H. The String Theory Landscape 42 1. Humans are irrelevant 12 1. Existence of de Sitter Vacua 43 2. Overdesign and Exaggerated Claims 12 2. Counting and Distributions 44 3. Necessary Ingredients 13 3. Is there a String Theory Landscape? 45 4. Other Potentially Habitable Universes 13 C. Is Life Generic in QFT? 15 V. The Standard Model in the Landscape 46 D. Levels of Anthropic Reasoning 17 A. The Gauge Sector 46 E. First Signs of a Landscape? 18 1. Gauge Group and Family Structure 46 1. Particle Physics 19 2. The Number of Families 47 2. Cosmology 19 3. Grand Unification in String Theory 48 3. The Cosmological Constant 21 4. Coupling Constant Unification 51 F. Possible Landscapes 24 5. The Fine-structure Constant 52 1. Fundamental Theories 24 B. Masses and Mixings 54 2. The r^oleof gravity 25 1. Anthropic Limits on Light Quark Masses 54 3. Other Landscapes? 25 2. The Top Quark Mass 61 4. Predictive Landscapes 26 5. Catastrophic Landscapes 27 3. Charged Lepton Masses 61 6. Expectations and implications 27 4. Masses and Mixings in the Landscape 62 5. Landscape vs. Symmetries 63 IV. String Theory 28 6. Neutrinos 64 A. Generalities 28 C. The Scales of the Standard Model 65 B. Modular invariance 29 1. Changing the Overall Scale 66 1. Finiteness and Space-time Supersymmetry 29 2. The Weak Scale 67 2. Ten-dimensional Strings 30 D. Axions 72 C. D-branes, p-forms and Fluxes 30 E. Variations in Constants of Nature 74 D. Dualities, M-theory and F-theory 31 E. The Bousso-Polchinski Mechanism 31 VI. Eternal Inflation 76 F. Four-Dimensional Strings and Compactifications 32 A. Tunneling 76 1. Landscape Studies versus Model Building 33 B. The Measure Problem. 77 2. General Features 33 1. The Dominant Vacuum 77 3. Calabi-Yau Compactifications 34 2. Local and Global Measures 78 4. Orbifold Compactifications 35 C. Paradoxes 79 5. The Beginning of the End of Uniqueness 35 1. The Youngness Problem 79 2. Boltzmann Brains 79 VII. The Cosmological Constant in the String Landscape 80 ∗ Extended version; see also www.nikhef.nl/∼t58/Landscape VIII. Conclusions 82 2 Acknowledgments 82 physics, we should focus on laws for which we have a solid underlying theoretical description. References 83 The most solid theoretical framework we know is that of quantum field theory, the language in which the Stan- dard Model of particle physics is written. Quantum field I. INTRODUCTION theory provides a huge number of theoretical possibili- ties, distinguished by some discrete and some continuous In popular accounts, our universe is usually described choices. The discrete choices are a small set of allowed as unimaginably huge. Indeed, during the last centuries Lorentz group representations, a choice of gauge symme- we have seen our horizon expand many orders of magni- tries (such as the strong and electroweak interactions), tude beyond any scale humans can relate to. and a choice of gauge-invariant couplings of the remain- But the earliest light we can see has traveled a mere ing matter. The continuous choices are the low-energy 13.8 billion years, just about three times the age of our parameters that are not yet fixed by the aforementioned planet. We might be able to look a little bit further than symmetries. In our universe we observe a certain choice that using intermediaries other than light, but soon we among all of these options, called the Standard Model, inevitably reach a horizon beyond which we cannot see. sketched in section II. But the quantum field theory we We cannot rule out the possibility that beyond that observe is just a single point in a discretely and contin- horizon there is just more of the same, or even nothing at uously infinite space. Infinitely many other choices are all, but widely accepted theories suggest something else. mathematically equally consistent. In the theory of inflation, our universe emerged from a Therefore the space of all quantum field theories pro- piece of a larger \space" that expanded by at least sixty vides the solid underlying description we need if we wish e-folds. Furthermore, in most theories of inflation our to consider alternatives to the laws of physics in our own universe is not a “one-off” event. It is much more plau- universe. This does not mean that nothing else could sible that the mechanism that gave rise to our universe vary, just that we cannot discuss other variations with was repeated a huge, even infinite, number of times. Our the same degree of confidence. But we can certainly theo- universe could just be an insignificant bubble in a gi- rize in a meaningful way about universes where the gauge gantic cosmological ensemble, a \multiverse". There are group or the fermion masses are different, or where the several classes of ideas that lead to such a picture, but matter does not even consist of quarks and leptons. there is no need to be specific here. The main point is We have no experimental evidence about the existence that other universes than our own may exist, at least in of such universes, although there are speculations about a mathematical sense. The universe we see is really just possible observations in the Cosmic Microwave Back- our universe. Well, not just ours, presumably. ground (see section III.E.2). We may get lucky, but our The existence of a multiverse may sound like specula- working hypothesis will be the pessimistic one that all tion, but one may as well ask how we can possibly be we can observe is our own universe. But even then, the certain that this is not true. Opponents and advocates claim that the only quantum field theory we can observe of the multiverse idea are both limited by the same hori- in principle, the Standard Model of particle physics, is zon. On whom rests the burden of proof? What is the also the only one that can exist mathematically, would most extraordinary statement: that what we can see is be truly extraordinary. precisely all that is possible, or that other possibilities Why should we even care about alternatives to our might exist? universe? One could adopt the point of view that the If we accept the logical possibility of a multiverse, the only reality is what we can observe, and that talking question arises in which respects other universes might about anything else amounts to leaving the realm of sci- be different. This obviously includes quantities that vary ence. But even then there is an important consequence. even within our own universe, such as the distribution If other sets of laws of physics are possible, even just of matter and the fluctuations in the cosmic microwave mathematically, this implies that our laws of physics can- background. But the cosmological parameters them- not be derived from first principles. They would be { at selves, and not just their fluctuations, might vary as well. least partly { environmental, and deducing them would And there may be more that varies: the \laws of physics" require some experimental or observational input. Cer- could be different. tainly this is not what many leading physicist have been Since we observe only one set of laws of physics it is a hoping for in the last decades. Undoubtedly, many of bit precarious to contemplate others. Could there exist them hoped for a negative answer to Einstein's famous alternatives to quantum mechanics, or could gravity ever question \I wonder if God had any choice in creating the be repulsive rather than attractive? None of that makes world". Consider for example Feynman's question about sense in any way we know, and hence it seems unlikely the value of the fine-structure constant α:\Immediately that anything useful can be learned by speculating about you would like to know where this number for a coupling this. If we want to consider variations in the laws of comes from: is it related to pi or perhaps to the base of 3 natural logarithms?". Indeed, there exist several fairly quest for a unique theory of all interactions. It is simply successful attempts to express α in terms of pure num- pointing out a glaring fallacy in that quest.
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