DOCSLIB.ORG

Non-Perturbative Type IIB Model Building in the F-Theory Framework

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Non-Perturbative Type IIB Model Building in the F-Theory Framework Dissertation der Fakult¨atf¨urPhysik der Ludwig-Maximilians-Universit¨atM¨unchen Nonperturbative Type IIB Model Building in the F-Theory Framework vorgelegt von Benjamin Helmut Friedrich Jurke aus Rheda-Wiedenbr¨uck M¨unchen 2010 Benjamin Helmut Friedrich Jurke Nonperturbative Type IIB Model Building in the F-Theory Framework 1. Gutachter: PD Dr. Ralph Blumenhagen Max-Planck-Institut f¨urPhysik, M¨unchen, Germany 2. Gutachter: Prof. Dr. Ilka Brunner Ludwig-Maximilians Universit¨atM¨unchen, Germany Datum der m¨undlichen Pr¨ufung: 28. Februar 2011 to whom it may concern... (and in particular my mother) Zusammenfassung Diese Dissertation behandelt das Gebiet der nicht-st¨orungstheoretischen Stringtheo- rie, die allgemein als vielversprechendster Ansatz zu einer konsistenten Beschreibung der Quantengravitation angesehen wird. Die f¨unfbekannten zehn-dimensionalen perturba- tiven Stringtheorien sind durch zahlreiche Dualit¨atenmiteinander verkn¨upft,sodass eine zugrundeliegende nicht-perturbative elf-dimensionale Theorie, genannt M-Theorie, postuliert wird. Uber¨ deren fundamentale Objekte ist aufgrund diverser technischer Schwierigkeiten allerdings nur wenig bekannt. Zur Typ-IIB-Stringtheorie existiert auch noch ein alternativer nicht-perturbativer Zugang, die F-Theorie. Diese geometrisiert die SL(2; Z)-Selbstdualit¨atder IIB-Theorie in Form einer elliptischen Faserung ¨uber der Raumzeit. Dar¨uber hinaus sind auch h¨oherdimensionaleObjekte wie etwa 7-Branen als Singularit¨atenin der geometrischen Beschreibung enthalten. Dieser formal elegante Ansatz erfordert allerdings einen großen technischen Aufwand in der Konstruktion akzeptabler Kompaktifizierungsgeometrien, da sehr viele Aspekte zwangsl¨aufiggleichzeitig behandelt werden m¨ussen. Daf¨urist aber eine im Vergleich zur perturbativen Stringtheorie einfachere Erzeugung essen- tieller Bausteine f¨urvereinheitlichte Theorien (GUTs) m¨oglich, beispielsweise bestimm- te Yukawa-Kopplungen oder Spinor-Darstellung. Ziel der Untersuchungen ist es daher eine vereinheitlichte Theorie innerhalb der F-Theorie zu formulieren, welche gewisse ph¨anomenologische Grundbedingungen erf¨ullt. Im Rahmen dieser Arbeit werden zun¨achst E3-Bran-Instantonen der Typ-IIB-String- theorie {{also vier-dimensionale Objekte, die sich ausschließlich um die unsichtbaren Dimensionen der Raumzeit wickeln {{mit M5-Branen in der F-Theorie in Beziehung gesetzt. Diese Objekte sind von großer Bedeutung f¨urdie Erzeugung ben¨otigterYukawa- Kopplungen oder etwa die Stabilisierung diverser freier Parameter einer Theorie. Be- stimmte Eigenschaften der M5-Branen erlauben es dann eine neue Bedingung zu for- mulieren, wann E3-Branen zum Superpotential beitragen k¨onnen. Im Anschluss zu dieser Analyse werden verschiedene Kompaktifizierungsgeometrien konstruiert und ihre prinzipielle Tauglichkeit zur Beschreibung grundlegend realistischer vereinheitlichter Theorien gepr¨uft. Ein entscheidender Punkt ist dabei den Eichfluss auf den enthaltenen 7-Branen korrekt zu beschreiben. Uber¨ die Methode der spek- tralen Uberdeckungen¨ {{die zun¨achst noch weiterer Verfeinerungen bedarf {{l¨asstsich vii viii dadurch dann chirale Materie erzeugen und zugleich die vereinheitlichte Eichgruppe zum Standardmodell hin reduzieren. Letztlich gelingt es in dieser Arbeit ein konkretes, ver- einheitlichtes Modell mit der Eichgruppe SU(5) im Rahmen der F-Theorie zu konstru- ieren, welches eine akzeptable Ph¨anomenologieaufzeigt und zudem die beobachteten drei chiralen Materie-Generationen reproduziert. Summary This dissertation is concerned with the topic of non-perturbative string theory, which is generally considered to be the most promising approach to a consistent description of quantum gravity. The five known 10-dimensional perturbative string theories are all interconnected by numerous dualities, such that an underlying non-perturbative 11- dimensional theory, called M-theory, is postulated. Due to several technical obstacles, little is known about the fundamental objects in this theory. There exists an alternative non-perturbative description to type IIB string theory, namely F-theory. Here the SL(2; Z) self-duality of IIB theory is geometrized in the form of an elliptic fibration over the space-time. Moreover, higher-dimensional objects like 7-branes are included via singularities into the geometric picture. This formally elegant description, however, requires significant technical effort for the construction of suitable compactification geometries, as many different aspects necessarily have to be dealt with at the same time. On the other hand, the generation of essential GUT building blocks like certain Yukawa couplings or spinor representations is easier com- pared to perturbative string theory. The goal of this study is therefore to formulate a unified theory within the framework of F-theory, that satisfies basic phenomenological constraints. Within this thesis, at first E3-brane instantons in type IIB string theory {{4-dimen- sional objects that are entirely wrapped around the invisible dimensions of space-time{{ are matched with M5-branes in F-theory. Such objects are of great importance in the generation of critical Yukawa couplings or the stabilization of the free parameters of a theory. Certain properties of M5-branes then allow to derive a new criterion for E3-branes to contribute to the superpotential. In the aftermath of this analysis, several compactification geometries are constructed and checked for basic properties that are relevant for semi-realistic unified model build- ing. An important aspect is the proper handling of the gauge flux on the 7-branes. Via the spectral cover description{{which at first requires further refinements{{chiral mat- ter can be generated and the unified gauge group can be broken to the Standard Model. Ultimately, in this thesis an explicit unified model based on the gauge group SU(5) is constructed within the F-theory framework, such that an acceptable phenomenology and the observed three chiral matter generations are obtained. ix Acknowledgments My particular gratitude goes to my advisor Ralph Blumenhagen, who constantly{{in his very own iconic way {{encouraged me and let me partake on his numerous insights into string theory and the required mathematics to delve deeper into the subject. I could not have asked for a more stimulating atmosphere in our work group during the countless discussions and research debates. I am also indebted to Dieter L¨ustfor his constant support and the effort he puts into providing all members of the string theory group with extraordinary opportunities for travel and research. I am very grateful to my collaborators Andr´esCollinucci, Thomas W. Grimm and Timo Weigand, from whom I learned at an unsurpassed pace especially during the first half of my PhD time. It was truly an unique opportunity to work with such a group of gifted people. Likewise, I would also like to thank my later collaborators and (former) office mates Thorsten Rahn and Helmut Roschy for the many productive and humorous hours back in the \cave", which was recently joined by Andreas Deser. Our time in the office was and still is a constant source of many memorable moments. Thanks to Oliver Schlotterer for many discussions (and disputes) as well as the oc- casional shared bottle of wine, a statement which in the same spirit can be extended to my old friend and former office mate Florian K¨uhnel. For comments on the manuscript of my thesis I would in particular like to thank Florian K¨uhnel,Thorsten Rahn, Helmut Roschy and Oliver Schlotterer. Furthermore, I would like to thank{{in alphabetical order{{Martin Ammon, Volker Braun, Ilka Brunner, James Gray, Michael Haack, James Halverson, Daniel H¨artl, Johannes Held, Johanna Knapp, Philipp Kostka, Sebastian Moster, Erik Plauschinn, Felix Rennecke, Maximilian Schmidt-Sommerfeld and Stephan Stieberger for various discussions and the sharing of thoughts and ideas. Moreover, I am grateful to my undergraduate advisor Reinhart K¨ogerlerfor pointing me in the right direction. An important cornerstone for me have always been my longstanding friends from back home, namely Daniel Altemeier, Cathrin and Sebastian Becker, Michael Brock- amp, Markus and Martin Menze, Christian Mester and Johannes R¨ottig.I am looking forward to each opportunity to meet the old circle again. I would also like to mention Philipp Nordhus. Words seem inadequate for the level of gratitude I have for my mother, who despite xi xii difficult circumstances made my venture into academia possible in the first place and supported me through all those years {{thanks, mum! Likewise, I am deeply thankful to my family, in particular my grandmother Gertrud as well as my godfathers Helmut and Friedrich for countless instances of help and support, which also includes my aunt Hannelore. Thanks for all your understanding and encouragement. This work is part of the String Theory program at the Max Planck Institute of Physics (MPP) in collab- oration with the Arnold Sommerfeld Center (ASC) of the Ludwig-Maximilians-Universit¨atM¨unchen (LMU) and supported by the International Max Planck Research School (IMPRS) on Elementary Particle Physics (EPP) of the Max Planck Society in Munich, Germany. Publications During the preparation of this thesis the following five research projects {{in col- laboration with the indicated authors {{and their respective results were published in peer-reviewed journals, listed in chronological order of publication: Global F-theory GUT model building and related matters: Ralph Blumenhagen, Thomas W. Grimm, Benjamin
Load more

Recommended publications
  • 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.
    [Show full text]
  • ABSTRACT Investigation Into Compactified Dimensions: Casimir
    ABSTRACT Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects Richard K. Obousy, Ph.D. Chairperson: Gerald B. Cleaver, Ph.D. The primary focus of this dissertation is the study of the Casimir effect and the possibility that this phenomenon may serve as a mechanism to mediate higher dimensional stability, and also as a possible mechanism for creating a small but non- zero vacuum energy density. In chapter one we review the nature of the quantum vacuum and discuss the different contributions to the vacuum energy density arising from different sectors of the standard model. Next, in chapter two, we discuss cosmology and the introduction of the cosmological constant into Einstein's field equations. In chapter three we explore the Casimir effect and study a number of mathematical techniques used to obtain a finite physical result for the Casimir energy. We also review the experiments that have verified the Casimir force. In chapter four we discuss the introduction of extra dimensions into physics. We begin by reviewing Kaluza Klein theory, and then discuss three popular higher dimensional models: bosonic string theory, large extra dimensions and warped extra dimensions. Chapter five is devoted to an original derivation of the Casimir energy we derived for the scenario of a higher dimensional vector field coupled to a scalar field in the fifth dimension. In chapter six we explore a range of vacuum scenarios and discuss research we have performed regarding moduli stability. Chapter seven explores a novel approach to spacecraft propulsion we have proposed based on the idea of manipulating the extra dimensions of string/M theory.
    [Show full text]
  • 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.
    [Show full text]
  • D-Branes in Topological Membranes
    OUTP/03–21P HWM–03–14 EMPG–03–13 hep-th/0308101 August 2003 D-BRANES IN TOPOLOGICAL MEMBRANES P. Castelo Ferreira Dep. de Matem´atica – Instituto Superior T´ecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal and PACT – University of Sussex, Falmer, Brighton BN1 9QJ, U.K. [email protected] I.I. Kogan Dept. of Physics, Theoretical Physics – University of Oxford, Oxford OX1 3NP, U.K. R.J. Szabo Dept. of Mathematics – Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K. [email protected] Abstract arXiv:hep-th/0308101v1 15 Aug 2003 It is shown how two-dimensional states corresponding to D-branes arise in orbifolds of topologically massive gauge and gravity theories. Brane vertex operators naturally appear in induced worldsheet actions when the three-dimensional gauge theory is minimally coupled to external charged matter and the orbifold relations are carefully taken into account. Boundary states corresponding to D-branes are given by vacuum wavefunctionals of the gauge theory in the presence of the matter, and their various constraints, such as the Cardy condition, are shown to arise through compatibility relations between the orbifold charges and bulk gauge invariance. We show that with a further conformally-invariant coupling to a dynamical massless scalar field theory in three dimensions, the brane tension is naturally set by the bulk mass scales and arises through dynamical mechanisms. As an auxilliary result, we show how to describe string descendent states in the three-dimensional theory through the construction of gauge-invariant excited wavefunctionals. Contents 1 INTRODUCTION AND SUMMARY 1 1.1 D-Branes ....................................
    [Show full text]
  • Universit`A Degli Studi Di Padova
    UNIVERSITA` DEGLI STUDI DI PADOVA Dipartimento di Fisica e Astronomia “Galileo Galilei” Corso di Laurea Magistrale in Fisica Tesi di Laurea Finite symmetry groups and orbifolds of two-dimensional toroidal conformal field theories Relatore Laureando Prof. Roberto Volpato Tommaso Macrelli Anno Accademico 2017/2018 Contents Introduction 5 1 Introduction to two dimensional Conformal Field Theory 7 1.1 The conformal group . .7 1.1.1 Conformal group in two dimensions . .9 1.2 Conformal invariance in two dimensions . 12 1.2.1 Fields and correlation functions . 12 1.2.2 Stress-energy tensor and conformal transformations . 13 1.2.3 Operator formalism: radial quantization . 14 1.3 General structure of a Conformal Field Theory in two dimensions . 16 1.3.1 Meromorphic Conformal Field Theory . 18 1.4 Examples . 22 1.4.1 Free boson . 22 1.4.2 Free Majorana fermion . 26 1.4.3 Ghost system . 27 2 Elements of String and Superstring Theory 28 2.1 Bosonic String Theory . 29 2.1.1 Classical Bosonic String . 29 2.1.2 Quantization . 31 2.1.3 BRST symmetry and Hilbert Space . 33 2.1.4 Spectrum of the Bosonic String . 34 2.1.5 What’s wrong with Bosonic String? . 36 2.2 Superstring Theory . 37 2.2.1 Introduction to Superstrings . 37 2.2.2 Heterotic String . 39 3 Compactifications of String Theory 41 3.1 An introduction: Kaluza-Klein compactification . 42 3.2 Free boson compactified on a circle . 43 3.2.1 Closed strings and T-Duality . 45 3.2.2 Enhanced symmetries at self-dual radius .
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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.....................
    [Show full text]
  • Free Lunch from T-Duality
    Free Lunch from T-Duality Ulrich Theis Institute for Theoretical Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D{07743 Jena, Germany [email protected] We consider a simple method of generating solutions to Einstein gravity coupled to a dilaton and a 2-form gauge potential in n dimensions, starting from an arbitrary (n m)- − dimensional Ricci-flat metric with m commuting Killing vectors. It essentially consists of a particular combination of coordinate transformations and T-duality and is related to the so-called null Melvin twists and TsT transformations. Examples obtained in this way include two charged black strings in five dimensions and a finite action configuration in three dimensions derived from empty flat space. The latter leads us to amend the effective action by a specific boundary term required for it to admit solutions with positive action. An extension of our method involving an S-duality transformation that is applicable to four-dimensional seed metrics produces further nontrivial solutions in five dimensions. 1 Introduction One of the most attractive features of string theory is that it gives rise to gravity: the low-energy effective action for the background fields on a string world-sheet is diffeomor- phism invariant and includes the Einstein-Hilbert term of general relativity. This effective action is obtained by integrating renormalization group beta functions whose vanishing is required for Weyl invariance of the world-sheet sigma model and can be interpreted as a set of equations of motion for the background fields. Solutions to these equations determine spacetimes in which the string propagates.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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>
    [Show full text]