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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 Life at the Interface of Particle Physics and String Theory [Word cloud by www.worldle.net] Last modified 23 September 2015 1 Life at the Interface of Particle Physics and String Theory A.N. Schellekensa;b;c a NIKHEF Theory Group, Kruislaan 409, 1098 SJ Amsterdam, The Netherlands b Instituto de F´ısica Fundamental, CSIC, Serrano 123, Madrid 28006, Spain c IMAPP, Radboud Universiteit, Nijmegen Abstract 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. 2 Contents 1 Introduction4 2 The Standard Model9 3 Anthropic Landscapes 17 3.1 What Can Be Varied?............................. 19 3.2 The Anthropocentric Trap........................... 20 3.2.1 Humans are irrelevant......................... 20 3.2.2 Overdesign and Exaggerated Claims................. 20 3.2.3 Necessary Ingredients.......................... 21 3.2.4 Other Potentially Habitable Universes................ 22 3.3 Is Life Generic in QFT?............................ 24 3.4 Levels of Anthropic Reasoning......................... 27 3.5 New Physics or Landscape Anarchy?..................... 29 3.6 Open Problems................................. 30 3.6.1 Particle Physics............................. 30 3.6.2 Cosmology................................ 31 3.6.3 The Cosmological Constant...................... 33 3.7 Possible Landscapes.............................. 38 3.7.1 Fundamental Theories......................... 38 3.7.2 The r^oleof gravity........................... 39 3.7.3 Other Landscapes?........................... 40 3.7.4 Predictive Landscapes......................... 41 3.7.5 Catastrophic Landscapes........................ 42 3.7.6 Expectations and implications..................... 43 4 String Theory 44 4.1 Generalities................................... 44 4.2 Modular invariance............................... 46 4.2.1 Finiteness and Space-time Supersymmetry.............. 46 4.2.2 Ten-dimensional Strings........................ 47 4.3 D-branes, p-forms and Fluxes......................... 48 4.4 Dualities, M-theory and F-theory....................... 49 4.5 The Bousso-Polchinski Mechanism....................... 49 4.6 Four-Dimensional Strings and Compactifications............... 51 4.6.1 Landscape Studies versus Model Building............... 51 4.6.2 General Features............................ 52 4.6.3 Calabi-Yau Compactifications..................... 53 4.6.4 Orbifold Compactifications....................... 54 4.6.5 The Beginning of the End of Uniqueness............... 55 4.6.6 Free Field Theory Constructions.................... 55 4.6.7 Early attempts at vacuum counting.................. 56 4.6.8 Meromorphic CFTs........................... 57 4.6.9 Gepner Models.............................. 58 4.6.10 New Directions in Heterotic strings.................. 59 4.6.11 Orientifolds and Intersecting Branes.................. 60 4.6.12 Decoupling Limits........................... 64 3 4.7 Non-supersymmetric strings.......................... 65 4.8 The String Theory Landscape......................... 66 4.8.1 Existence of de Sitter Vacua...................... 67 4.8.2 Counting and Distributions...................... 69 4.8.3 Is there a String Theory Landscape?................. 70 5 The Standard Model in the Landscape 71 5.1 The Gauge Sector................................ 71 5.1.1 Gauge Group and Family Structure.................. 71 5.1.2 The Number of Families........................ 72 5.1.3 Grand Unification in String Theory.................. 74 5.1.4 Coupling Constant Unification..................... 79 5.1.5 The Fine-structure Constant...................... 81 5.2 Masses and Mixings............................... 83 5.2.1 Anthropic Limits on Light Quark Masses............... 83 5.2.2 The Top Quark Mass.......................... 96 5.2.3 Charged Lepton Masses........................ 97 5.2.4 Masses and Mixings in the Landscape................. 97 5.2.5 Landscape vs. Symmetries....................... 99 5.2.6 Neutrinos................................ 101 5.3 The Scales of the Standard Model....................... 103 5.3.1 Changing the Overall Scale...................... 104 5.3.2 The Weak Scale............................. 106 5.4 Axions...................................... 113 5.5 Variations in Constants of Nature....................... 116 6 Eternal Inflation 119 6.1 Tunneling.................................... 119 6.2 The Measure Problem.............................. 120 6.2.1 The Dominant Vacuum......................... 121 6.2.2 Local and Global Measures....................... 122 6.3 Paradoxes.................................... 122 6.3.1 The Youngness Problem........................ 122 6.3.2 Boltzmann Brains............................ 123 7 The Cosmological Constant in the String Landscape 124 8 Conclusions 127 1 Introduction In popular accounts, our universe is usually described as unimaginably huge. Indeed, during the last centuries we have seen our horizon expand many orders of magnitude beyond any scale humans can relate to. But the earliest light we can see has traveled a mere 13.8 billion years, just about three times the age of our planet. We might be able to look a little bit further than that using intermediaries other than light, but soon we inevitably reach a horizon beyond which we cannot see. 4 We cannot rule out the possibility that beyond that horizon there is just more of the same, or even nothing at all, but widely accepted theories suggest something else. In the theory of inflation, our universe emerged from a piece of a larger \space" that expanded by at least sixty e-folds. Furthermore, in most theories of inflation our universe is not a “one-off” event. It is much more plausible that the mechanism that gave rise to our universe was repeated a huge, even infinite, number of times. Our universe could just be an insignificant bubble in a gigantic cosmological ensemble, a \multiverse". There are several classes of ideas that lead to such a picture, but there is no need to be specific here. The main point is that other universes than our own may exist, at least in a mathematical sense. The universe we see is really just our universe. Well, not just ours, presumably. The existence of a multiverse may sound like speculation, but one may as well ask how we can possibly be certain that this is not true. Opponents and advocates of the multiverse idea are both limited by the same horizon. On whom rests the burden of proof? What is the most extraordinary statement: that what we can see is precisely all that is possible, or that other possibilities might exist? If we accept the logical possibility of a multiverse, the question arises in which respects other universes might be different. This obviously includes quantities that vary even within our own universe, such as the distribution of matter and the fluctuations in the cosmic microwave background. But the cosmological parameters themselves, and not just their fluctuations, might vary as well. And there may be more that varies: the \laws of physics" could be different. Since we observe only one set of laws of physics it is a bit precarious to contemplate others. Could there exist alternatives to quantum mechanics, or could gravity ever be repulsive rather than attractive? None of that makes sense in any way we know, and hence it seems unlikely that anything useful can be learned by speculating about this. If we want to consider variations in the laws of physics, we should focus on laws for which we have a solid underlying theoretical description. The most solid theoretical framework we know is that of quantum field theory, the language in which the Standard Model of particle physics is written. Quantum field the- ory provides a huge number of theoretical possibilities, distinguished by some discrete and some continuous choices. The discrete choices are a small set of allowed Lorentz group representations, a choice of gauge symmetries (such as the strong and electroweak interac- tions), and a choice of gauge-invariant couplings of the remaining matter. The continuous choices are the low-energy parameters that are not yet fixed by the aforementioned sym- metries. In our universe we observe a certain choice among all of these options, called the Standard Model, sketched in section2. But the quantum field theory we observe is just a single point in a discretely and continuously infinite space. Infinitely many other choices are mathematically equally consistent. Therefore the space of all quantum field theories provides the solid underlying descrip- tion we need if we wish to consider alternatives to the laws of physics in our own universe. This does not mean that nothing else could vary, just that we cannot discuss other vari- ations with the same
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