Big Numbers in String Theory” but Hindawi Insisted That I Change the Title to Something More “Scientific”
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A String Landscape Perspective on Naturalness Outline • Preliminaries
A String Landscape Perspective on Naturalness A. Hebecker (Heidelberg) Outline • Preliminaries (I): The problem(s) and the multiverse `solution' • Preliminaries (II): From field theory to quantum gravity (String theory in 10 dimensions) • Compactifications to 4 dimensions • The (flux-) landscape • Eternal inflation, multiverse, measure problem The two hierarchy/naturalness problems • A much simplified basic lagrangian is 2 2 2 2 4 L ∼ MP R − Λ − jDHj + mhjHj − λjHj : • Assuming some simple theory with O(1) fundamental parameters at the scale E ∼ MP , we generically expectΛ and mH of that order. • For simplicity and because it is experimentally better established, I will focus in on theΛ-problem. (But almost all that follows applies to both problems!) The multiverse `solution' • It is quite possible that in the true quantum gravity theory, Λ comes out tiny as a result of an accidental cancellation. • But, we perceive that us unlikely. • By contrast, if we knew there were 10120 valid quantum gravity theories, we would be quite happy assuming that one of them has smallΛ. (As long as the calculations giving Λ are sufficiently involved to argue for Gaussian statisics of the results.) • Even better (since in principle testable): We could have one theory with 10120 solutions with differentΛ. Λ-values ! The multiverse `solution' (continued) • This `generic multiverse logic' has been advertised long before any supporting evidence from string theory existed. This goes back at least to the 80's and involves many famous names: Barrow/Tipler , Tegmark , Hawking , Hartle , Coleman , Weinberg .... • Envoking the `Anthropic Principle', [the selection of universes by demanding features which we think are necessary for intelligent life and hence for observers] it is then even possible to predict certain observables. -
TASI Lectures on String Compactification, Model Building
CERN-PH-TH/2005-205 IFT-UAM/CSIC-05-044 TASI lectures on String Compactification, Model Building, and Fluxes Angel M. Uranga TH Unit, CERN, CH-1211 Geneve 23, Switzerland Instituto de F´ısica Te´orica, C-XVI Universidad Aut´onoma de Madrid Cantoblanco, 28049 Madrid, Spain angel.uranga@cern,ch We review the construction of chiral four-dimensional compactifications of string the- ory with different systems of D-branes, including type IIA intersecting D6-branes and type IIB magnetised D-branes. Such models lead to four-dimensional theories with non-abelian gauge interactions and charged chiral fermions. We discuss the application of these techniques to building of models with spectrum as close as possible to the Stan- dard Model, and review their main phenomenological properties. We finally describe how to implement the tecniques to construct these models in flux compactifications, leading to models with realistic gauge sectors, moduli stabilization and supersymmetry breaking soft terms. Lecture 1. Model building in IIA: Intersecting brane worlds 1 Introduction String theory has the remarkable property that it provides a description of gauge and gravitational interactions in a unified framework consistently at the quantum level. It is this general feature (beyond other beautiful properties of particular string models) that makes this theory interesting as a possible candidate to unify our description of the different particles and interactions in Nature. Now if string theory is indeed realized in Nature, it should be able to lead not just to `gauge interactions' in general, but rather to gauge sectors as rich and intricate as the gauge theory we know as the Standard Model of Particle Physics. -
String Theory for Pedestrians
String Theory for Pedestrians – CERN, Jan 29-31, 2007 – B. Zwiebach, MIT This series of 3 lecture series will cover the following topics 1. Introduction. The classical theory of strings. Application: physics of cosmic strings. 2. Quantum string theory. Applications: i) Systematics of hadronic spectra ii) Quark-antiquark potential (lattice simulations) iii) AdS/CFT: the quark-gluon plasma. 3. String models of particle physics. The string theory landscape. Alternatives: Loop quantum gravity? Formulations of string theory. 1 Introduction For the last twenty years physicists have investigated String Theory rather vigorously. Despite much progress, the basic features of the theory remain a mystery. In the late 1960s, string theory attempted to describe strongly interacting particles. Along came Quantum Chromodynamics (QCD)– a theory of quarks and gluons – and despite their early promise, strings faded away. This time string theory is a credible candidate for a theory of all interactions – a unified theory of all forces and matter. Additionally, • Through the AdS/CFT correspondence, it is a valuable tool for the study of theories like QCD. • It has helped understand the origin of the Bekenstein-Hawking entropy of black holes. • Finally, it has inspired many of the scenarios for physics Beyond the Standard Model of Particle physics. 2 Greatest problem of twentieth century physics: the incompatibility of Einstein’s General Relativity and the principles of Quantum Mechanics. String theory appears to be the long-sought quantum mechanical theory of gravity and other interactions. It is almost certain that string theory is a consistent theory. It is less certain that it describes our real world. -
The String Theory Landscape and Cosmological Inflation
The String Theory Landscape and Cosmological Inflation Background Image: Planck Collaboration and ESA The String Theory Landscape and Cosmological Inflation Outline • Preliminaries: From Field Theory to Quantum Gravity • String theory in 10 dimensions { a \reminder" • Compactifications to 4 dimensions • The (flux-) landscape • Eternal inflation and the multiverse • Slow-roll inflation in our universe • Recent progress in inflation in string theory From Particles/Fields to Quantum Gravity • Naive picture of particle physics: • Theoretical description: Quantum Field Theory • Usually defined by an action: Z 4 µρ νσ S(Q)ED = d x Fµν Fρσ g g with T ! @Aµ @Aν 0 E Fµν = − = @xν @xµ −E "B Gravity is in principle very similar: • The metric gµν becomes a field, more precisely Z 4 p SG = d x −g R[gµν] ; where R measures the curvature of space-time • In more detail: gµν = ηµν + hµν • Now, with hµν playing the role of Aµ, we find Z 4 ρ µν SG = d x (@ρhµν)(@ h ) + ··· • Waves of hµν correspond to gravitons, just like waves of Aµ correspond to photons • Now, replace SQED with SStandard Model (that's just a minor complication....) and write S = SG + SSM : This could be our `Theory of Everything', but there are divergences .... • Divergences are a hard but solvable problem for QFT • However, these very same divergences make it very difficult to even define quantum gravity at E ∼ MPlanck String theory: `to know is to love' • String theory solves this problem in 10 dimensions: • The divergences at ~k ! 1 are now removed (cf. Timo Weigand's recent colloquium talk) • Thus, in 10 dimensions but at low energy (E 1=lstring ), we get an (essentially) unique 10d QFT: µνρ µνρ L = R[gµν] + FµνρF + HµνρH + ··· `Kaluza-Klein Compactification’ to 4 dimensions • To get the idea, let us first imagine we had a 2d theory, but need a 1d theory • We can simply consider space to have the form of a cylinder or `the surface of a rope': Image by S. -
Lectures on Naturalness, String Landscape and Multiverse
Lectures on Naturalness, String Landscape and Multiverse Arthur Hebecker Institute for Theoretical Physics, Heidelberg University, Philosophenweg 19, D-69120 Heidelberg, Germany 24 August, 2020 Abstract The cosmological constant and electroweak hierarchy problem have been a great inspira- tion for research. Nevertheless, the resolution of these two naturalness problems remains mysterious from the perspective of a low-energy effective field theorist. The string theory landscape and a possible string-based multiverse offer partial answers, but they are also controversial for both technical and conceptual reasons. The present lecture notes, suitable for a one-semester course or for self-study, attempt to provide a technical introduction to these subjects. They are aimed at graduate students and researchers with a solid back- ground in quantum field theory and general relativity who would like to understand the string landscape and its relation to hierarchy problems and naturalness at a reasonably technical level. Necessary basics of string theory are introduced as part of the course. This text will also benefit graduate students who are in the process of studying string theory arXiv:2008.10625v3 [hep-th] 27 Jul 2021 at a deeper level. In this case, the present notes may serve as additional reading beyond a formal string theory course. Preface This course intends to give a concise but technical introduction to `Physics Beyond the Standard Model' and early cosmology as seen from the perspective of string theory. Basics of string theory will be taught as part of the course. As a central physics theme, the two hierarchy problems (of the cosmological constant and of the electroweak scale) will be discussed in view of ideas like supersymmetry, string theory landscape, eternal inflation and multiverse. -
Introduction to String Theory A.N
Introduction to String Theory A.N. Schellekens Based on lectures given at the Radboud Universiteit, Nijmegen Last update 6 July 2016 [Word cloud by www.worldle.net] Contents 1 Current Problems in Particle Physics7 1.1 Problems of Quantum Gravity.........................9 1.2 String Diagrams................................. 11 2 Bosonic String Action 15 2.1 The Relativistic Point Particle......................... 15 2.2 The Nambu-Goto action............................ 16 2.3 The Free Boson Action............................. 16 2.4 World sheet versus Space-time......................... 18 2.5 Symmetries................................... 19 2.6 Conformal Gauge................................ 20 2.7 The Equations of Motion............................ 21 2.8 Conformal Invariance.............................. 22 3 String Spectra 24 3.1 Mode Expansion................................ 24 3.1.1 Closed Strings.............................. 24 3.1.2 Open String Boundary Conditions................... 25 3.1.3 Open String Mode Expansion..................... 26 3.1.4 Open versus Closed........................... 26 3.2 Quantization.................................. 26 3.3 Negative Norm States............................. 27 3.4 Constraints................................... 28 3.5 Mode Expansion of the Constraints...................... 28 3.6 The Virasoro Constraints............................ 29 3.7 Operator Ordering............................... 30 3.8 Commutators of Constraints.......................... 31 3.9 Computation of the Central Charge..................... -
Buffy & Angel Watching Order
Start with: End with: BtVS 11 Welcome to the Hellmouth Angel 41 Deep Down BtVS 11 The Harvest Angel 41 Ground State BtVS 11 Witch Angel 41 The House Always Wins BtVS 11 Teacher's Pet Angel 41 Slouching Toward Bethlehem BtVS 12 Never Kill a Boy on the First Date Angel 42 Supersymmetry BtVS 12 The Pack Angel 42 Spin the Bottle BtVS 12 Angel Angel 42 Apocalypse, Nowish BtVS 12 I, Robot... You, Jane Angel 42 Habeas Corpses BtVS 13 The Puppet Show Angel 43 Long Day's Journey BtVS 13 Nightmares Angel 43 Awakening BtVS 13 Out of Mind, Out of Sight Angel 43 Soulless BtVS 13 Prophecy Girl Angel 44 Calvary Angel 44 Salvage BtVS 21 When She Was Bad Angel 44 Release BtVS 21 Some Assembly Required Angel 44 Orpheus BtVS 21 School Hard Angel 45 Players BtVS 21 Inca Mummy Girl Angel 45 Inside Out BtVS 22 Reptile Boy Angel 45 Shiny Happy People BtVS 22 Halloween Angel 45 The Magic Bullet BtVS 22 Lie to Me Angel 46 Sacrifice BtVS 22 The Dark Age Angel 46 Peace Out BtVS 23 What's My Line, Part One Angel 46 Home BtVS 23 What's My Line, Part Two BtVS 23 Ted BtVS 71 Lessons BtVS 23 Bad Eggs BtVS 71 Beneath You BtVS 24 Surprise BtVS 71 Same Time, Same Place BtVS 24 Innocence BtVS 71 Help BtVS 24 Phases BtVS 72 Selfless BtVS 24 Bewitched, Bothered and Bewildered BtVS 72 Him BtVS 25 Passion BtVS 72 Conversations with Dead People BtVS 25 Killed by Death BtVS 72 Sleeper BtVS 25 I Only Have Eyes for You BtVS 73 Never Leave Me BtVS 25 Go Fish BtVS 73 Bring on the Night BtVS 26 Becoming, Part One BtVS 73 Showtime BtVS 26 Becoming, Part Two BtVS 74 Potential BtVS 74 -
The Romance Between Maths and Physics
The Romance Between Maths and Physics Miranda C. N. Cheng University of Amsterdam Very happy to be back in NTU indeed! Question 1: Why is Nature predictable at all (to some extent)? Question 2: Why are the predictions in the form of mathematics? the unreasonable effectiveness of mathematics in natural sciences. Eugene Wigner (1960) First we resorted to gods and spirits to explain the world , and then there were ….. mathematicians?! Physicists or Mathematicians? Until the 19th century, the relation between physical sciences and mathematics is so close that there was hardly any distinction made between “physicists” and “mathematicians”. Even after the specialisation starts to be made, the two maintain an extremely close relation and cannot live without one another. Some of the love declarations … Dirac (1938) If you want to be a physicist, you must do three things— first, study mathematics, second, study more mathematics, and third, do the same. Sommerfeld (1934) Our experience up to date justifies us in feeling sure that in Nature is actualized the ideal of mathematical simplicity. It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them, which gives us the key to understanding nature… In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed. Einstein (1934) Indeed, the most irresistible reductionistic charm of physics, could not have been possible without mathematics … Love or Hate? It’s Complicated… In the era when Physics seemed invincible (think about the standard model), they thought they didn’t need each other anymore. -
Mathematically Talented Women in Hollywood: Fred in Angel
Mathematically Talented Women in Hollywood: Fred in Angel Sarah J. Greenwald and Jill E. Thomley Appalachian State University Introduction Individual faculty such as those represented in this volume have used popular culture in the class- room to alleviate math anxiety and to help students connect to significant mathematics. Recent educational initiatives such as We All Use Math Every Day [12], co-sponsored by CBS, Texas In- struments, and the National Council of Teachers of Mathematics, and MathMovesU [31], sponsored by Raytheon, strive to change attitudes and attract students to mathematics by capitalizing on student enjoyment of celebrities and popular culture. At the same time, Hollywood has increased its use of math and mathematicians, but some of those representations may not be all that positive for attracting students to mathematics. Others have examined the stereotype of the mentally ill mathematician (e.g., [25]), which may make it harder for students to identify with mathematicians. In this article we discuss the representations of mathematically talented women in Hollywood and provide a framework for examining the messages they may convey to the public and our students as we examine the example of physicist Fred Burkle in the television show Angel [1]. Unlike more recent representations of women mathematicians, such as Amita in NUMB3RS, which are aimed at a more mature audience, Angel aired on the WB network from October 1999 to May 2004 as part of a lineup of programs specifically targeted at teens and young adults. It is for this reason, and also because Fred’s experiences provide a rich context to discuss a variety of issues related to women in mathematics, that we chose Fred as a case study. -
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. -
Bachas: Massive Ads Gravity from String Theory
Massive AdS Gravity from String Theory Costas BACHAS (ENS, Paris) Conference on "Geometry and Strings’’ Schloss Ringberg, July 23 - 27, 2018 Based on two papers with Ioannis Lavdas arXiv: 1807.00591 arXiv: 1711.11372 Earlier work with John Estes arXiv: 1103.2800 If I have time, I may also comment briefly on arXiv: 1711.06722 with Bianchi & Hanany Plan of Talk 1. Foreword 2. g-Mass from holography 3. Representation merging 4. Review of N=4 AdS4/CFT3 5. g-Mass operator 6. `Scottish Bagpipes’ 7. 3 rewritings & bigravity 8. Final remarks 1 Foreword An old question: Can gravity be `higgsed’ (become massive) ? Extensive (recent & less recent) literature: Pauli, Fierz, Proc.Roy.Soc. 1939 . Nice reviews: Hinterblicher 1105.3735; de Rham 1401.4173 Schmidt-May & von Strauss 1512.00021 The question is obviously interesting, since any sound IR modification of General Relativity could have consequences for cosmology [degravitating dark energy? `mimicking dark matter’ ? . ] The main messages of this talk : — Massive AdS Gravity is part of the string-theory landscape — A quasi-universal, quantized formula for the mass Setting is 10d IIB sugra, and holographic dual CFTs If <latexit sha1_base64="RY3Mceo40A2JogR2P79cFMHL7hM=">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</latexit> -
Tensor Modes on the String Theory Landscape Arxiv:1206.4034V1 [Hep
Tensor modes on the string theory landscape Alexander Westphal Deutsches Elektronen-Synchrotron DESY, Theory Group, D-22603 Hamburg, Germany We attempt an estimate for the distribution of the tensor mode fraction r over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory. arXiv:1206.4034v1 [hep-th] 18 Jun 2012 June 19, 2012 Contents 1 Introduction and Motivation 2 2 Assumptions 5 2.1 Need for symmetry . 5 2.2 Properties of scalar fields in compactified string theory . 7 2.3 Populating vacua { tunneling and quantum diffusion . 8 3 An almost argument { field displacement is expensive 11 4 Counting ... 24 4.1 Eternity . 24 4.2 Democracy { tumbling down the rabbit hole . 26 4.3 Vacuum energy distribution . 31 4.4 Multitude . 32 4.5 An accessible sector of landscape . 36 5 Discussion 38 A Suppression of uphill tunneling 41 A.1 CdL tunneling in the thin-wall approximation . 41 A.2 CdL tunneling away from the thin-wall approximation . 42 A.3 Hawking-Moss tunneling - the 'no-wall' limit .