Double Field Theory on Group Manifolds
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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. -
Introduction to Conformal Field Theory and String
SLAC-PUB-5149 December 1989 m INTRODUCTION TO CONFORMAL FIELD THEORY AND STRING THEORY* Lance J. Dixon Stanford Linear Accelerator Center Stanford University Stanford, CA 94309 ABSTRACT I give an elementary introduction to conformal field theory and its applications to string theory. I. INTRODUCTION: These lectures are meant to provide a brief introduction to conformal field -theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available (or almost available), and most of these go in to much more detail than I will be able to here. Those reviews con- centrating on the CFT side of the subject include refs. 1,2,3,4; those emphasizing string theory include refs. 5,6,7,8,9,10,11,12,13 I will start with a little pre-history of string theory to help motivate the sub- ject. In the 1960’s it was noticed that certain properties of the hadronic spectrum - squared masses for resonances that rose linearly with the angular momentum - resembled the excitations of a massless, relativistic string.14 Such a string is char- *Work supported in by the Department of Energy, contract DE-AC03-76SF00515. Lectures presented at the Theoretical Advanced Study Institute In Elementary Particle Physics, Boulder, Colorado, June 4-30,1989 acterized by just one energy (or length) scale,* namely the square root of the string tension T, which is the energy per unit length of a static, stretched string. For strings to describe the strong interactions fi should be of order 1 GeV. Although strings provided a qualitative understanding of much hadronic physics (and are still useful today for describing hadronic spectra 15 and fragmentation16), some features were hard to reconcile. -
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..................... -
Achievements, Progress and Open Questions in String Field Theory Strings 2021 ICTP-SAIFR, S˜Ao Paulo June 22, 2021
Achievements, Progress and Open Questions in String Field Theory Strings 2021 ICTP-SAIFR, S˜ao Paulo June 22, 2021 Yuji Okawa and Barton Zwiebach 1 Achievements We consider here instances where string field theory provided the answer to physical open questions. • Tachyon condensation, tachyon vacuum, tachyon conjectures The tachyon conjectures (Sen, 1999) posited that: (a) The tachyon potential has a locally stable minimum, whose energy density measured with respect to that of the unstable critical point, equals minus the tension of the D25-brane (b) Lower-dimensional D-branes are solitonic solutions of the string theory on the back- ground of a D25-brane. (c) The locally stable vacuum of the system is the closed string vac- uum; it has no open string excitations exist. Work in SFT established these conjectures by finding the tachyon vac- uum, first numerically, and then analytically (Schnabl, 2005). These are non-perturbative results. 2 • String field theory is the first complete definition of string pertur- bation theory. The first-quantized world-sheet formulation of string theory does not define string perturbation theory completely: – No systematic way of dealing with IR divergences. – No systematic way of dealing with S-matrix elements for states that undergo mass renormalization. Work of A. Sen and collaborators demonstrating this: (a) One loop-mass renormalization of unstable particles in critical string theories. (b) Fixing ambiguities in two-dimensional string theory: For the one- instanton contribution to N-point scattering amplitudes there are four undetermined constants (Balthazar, Rodriguez, Yin, 2019). Two of them have been fixed with SFT (Sen 2020) (c) Fixing the normalization of Type IIB D-instanton amplitudes (Sen, 2021). -
Chapter 9: the 'Emergence' of Spacetime in String Theory
Chapter 9: The `emergence' of spacetime in string theory Nick Huggett and Christian W¨uthrich∗ May 21, 2020 Contents 1 Deriving general relativity 2 2 Whence spacetime? 9 3 Whence where? 12 3.1 The worldsheet interpretation . 13 3.2 T-duality and scattering . 14 3.3 Scattering and local topology . 18 4 Whence the metric? 20 4.1 `Background independence' . 21 4.2 Is there a Minkowski background? . 24 4.3 Why split the full metric? . 27 4.4 T-duality . 29 5 Quantum field theoretic considerations 29 5.1 The graviton concept . 30 5.2 Graviton coherent states . 32 5.3 GR from QFT . 34 ∗This is a chapter of the planned monograph Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity, co-authored by Nick Huggett and Christian W¨uthrich and under contract with Oxford University Press. More information at www.beyondspacetime.net. The primary author of this chapter is Nick Huggett ([email protected]). This work was sup- ported financially by the ACLS and the John Templeton Foundation (the views expressed are those of the authors not necessarily those of the sponsors). We want to thank Tushar Menon and James Read for exceptionally careful comments on a draft this chapter. We are also grateful to Niels Linnemann for some helpful feedback. 1 6 Conclusions 35 This chapter builds on the results of the previous two to investigate the extent to which spacetime might be said to `emerge' in perturbative string the- ory. Our starting point is the string theoretic derivation of general relativity explained in depth in the previous chapter, and reviewed in x1 below (so that the philosophical conclusions of this chapter can be understood by those who are less concerned with formal detail, and so skip the previous one). -
String Field Theory, Nucl
1 String field theory W. TAYLOR MIT, Stanford University SU-ITP-06/14 MIT-CTP-3747 hep-th/0605202 Abstract This elementary introduction to string field theory highlights the fea- tures and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string the- ory as a field theory in space-time with an infinite number of massive fields. Although existing constructions of string field theory require ex- panding around a fixed choice of space-time background, the theory is in principle background-independent, in the sense that different back- grounds can be realized as different field configurations in the theory. String field theory is the only string formalism developed so far which, in principle, has the potential to systematically address questions involv- ing multiple asymptotically distinct string backgrounds. Thus, although it is not yet well defined as a quantum theory, string field theory may eventually be helpful for understanding questions related to cosmology arXiv:hep-th/0605202v2 28 Jun 2006 in string theory. 1.1 Introduction In the early days of the subject, string theory was understood only as a perturbative theory. The theory arose from the study of S-matrices and was conceived of as a new class of theory describing perturbative interactions of massless particles including the gravitational quanta, as well as an infinite family of massive particles associated with excited string states. In string theory, instead of the one-dimensional world line 1 2 W. Taylor of a pointlike particle tracing out a path through space-time, a two- dimensional surface describes the trajectory of an oscillating loop of string, which appears pointlike only to an observer much larger than the string. -
Exceptional Field Theory and Supergravity Arnaud Baguet
Exceptional Field Theory and Supergravity Arnaud Baguet To cite this version: Arnaud Baguet. Exceptional Field Theory and Supergravity. High Energy Physics - Experiment [hep-ex]. Université de Lyon, 2017. English. NNT : 2017LYSEN022. tel-01563063 HAL Id: tel-01563063 https://tel.archives-ouvertes.fr/tel-01563063 Submitted on 17 Jul 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Numéro National de Thèse : 2017LYSEN022 Thèse de Doctorat de l’Université de Lyon opérée par l’École Normale Supérieure de Lyon École Doctorale 52 École Doctorale de Physique et d’Astrophysique de Lyon Soutenue publiquement le 30/06/2017, par : Arnaud Baguet Exceptional Field Theory and Supergravity - Théorie des Champs Exceptionnels et Supergravité Devant le jury composé de : Martin Cederwall Chalmers University of Technology Rapporteur François Delduc École Normale Supérieure de Lyon Examinateur Axel Kleinschmidt Max Planck Institute Postdam Rapporteur Michela Petrini Université Pierre et Marie Curie Examinatrice Henning Samtleben École Normale Supérieure de Lyon Directeur Contents 1 Introduction 9 1.1 String theory, dualities and supergravity . 11 1.2 The bosonic string . 13 1.3 Compactification and T-duality . 18 1.4 Double Field Theory . 21 1.5 Exceptional Field Theory . -
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. -
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.