Extra Dimensions
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Symmetry and Gravity
universe Article Making a Quantum Universe: Symmetry and Gravity Houri Ziaeepour 1,2 1 Institut UTINAM, CNRS UMR 6213, Observatoire de Besançon, Université de Franche Compté, 41 bis ave. de l’Observatoire, BP 1615, 25010 Besançon, France; [email protected] or [email protected] 2 Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Dorking GU5 6NT, UK Received: 05 September 2020; Accepted: 17 October 2020; Published: 23 October 2020 Abstract: So far, none of attempts to quantize gravity has led to a satisfactory model that not only describe gravity in the realm of a quantum world, but also its relation to elementary particles and other fundamental forces. Here, we outline the preliminary results for a model of quantum universe, in which gravity is fundamentally and by construction quantic. The model is based on three well motivated assumptions with compelling observational and theoretical evidence: quantum mechanics is valid at all scales; quantum systems are described by their symmetries; universe has infinite independent degrees of freedom. The last assumption means that the Hilbert space of the Universe has SUpN Ñ 8q – area preserving Diff.pS2q symmetry, which is parameterized by two angular variables. We show that, in the absence of a background spacetime, this Universe is trivial and static. Nonetheless, quantum fluctuations break the symmetry and divide the Universe to subsystems. When a subsystem is singled out as reference—observer—and another as clock, two more continuous parameters arise, which can be interpreted as distance and time. We identify the classical spacetime with parameter space of the Hilbert space of the Universe. -
Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings. -
Loop Quantum Cosmology, Modified Gravity and Extra Dimensions
universe Review Loop Quantum Cosmology, Modified Gravity and Extra Dimensions Xiangdong Zhang Department of Physics, South China University of Technology, Guangzhou 510641, China; [email protected] Academic Editor: Jaume Haro Received: 24 May 2016; Accepted: 2 August 2016; Published: 10 August 2016 Abstract: Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans–Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed. Keywords: loop quantum cosmology; singularity resolution; effective equation 1. Introduction Loop quantum gravity (LQG) is a quantum gravity scheme that tries to quantize general relativity (GR) with the nonperturbative techniques consistently [1–4]. Many issues of LQG have been carried out in the past thirty years. In particular, among these issues, loop quantum cosmology (LQC), which is the cosmological sector of LQG has received increasing interest and has become one of the most thriving and fruitful directions of LQG [5–9]. It is well known that GR suffers singularity problems and this, in turn, implies that our universe also has an infinitely dense singularity point that is highly unphysical. -
Aspects of Loop Quantum Gravity
Aspects of loop quantum gravity Alexander Nagen 23 September 2020 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London 1 Contents 1 Introduction 4 2 Classical theory 12 2.1 The ADM / initial-value formulation of GR . 12 2.2 Hamiltonian GR . 14 2.3 Ashtekar variables . 18 2.4 Reality conditions . 22 3 Quantisation 23 3.1 Holonomies . 23 3.2 The connection representation . 25 3.3 The loop representation . 25 3.4 Constraints and Hilbert spaces in canonical quantisation . 27 3.4.1 The kinematical Hilbert space . 27 3.4.2 Imposing the Gauss constraint . 29 3.4.3 Imposing the diffeomorphism constraint . 29 3.4.4 Imposing the Hamiltonian constraint . 31 3.4.5 The master constraint . 32 4 Aspects of canonical loop quantum gravity 35 4.1 Properties of spin networks . 35 4.2 The area operator . 36 4.3 The volume operator . 43 2 4.4 Geometry in loop quantum gravity . 46 5 Spin foams 48 5.1 The nature and origin of spin foams . 48 5.2 Spin foam models . 49 5.3 The BF model . 50 5.4 The Barrett-Crane model . 53 5.5 The EPRL model . 57 5.6 The spin foam - GFT correspondence . 59 6 Applications to black holes 61 6.1 Black hole entropy . 61 6.2 Hawking radiation . 65 7 Current topics 69 7.1 Fractal horizons . 69 7.2 Quantum-corrected black hole . 70 7.3 A model for Hawking radiation . 73 7.4 Effective spin-foam models . -
TASI Lectures on Extra Dimensions and Branes
hep-ph/0404096 TASI Lectures on Extra Dimensions and Branes∗ Csaba Cs´aki Institute of High Energy Phenomenology, Newman Laboratory of Elementary Particle Physics, Cornell University, Ithaca, NY 14853 [email protected] Abstract This is a pedagogical introduction into theories with branes and extra dimensions. We first discuss the construction of such models from an effective field theory point of view, and then discuss large extra dimensions and some of their phenomenological consequences. Various possible phenomena (split fermions, mediation of supersym- metry breaking and orbifold breaking of symmetries) are discussed next. The second arXiv:hep-ph/0404096v1 9 Apr 2004 half of this review is entirely devoted to warped extra dimensions, including the con- struction of the Randall-Sundrum solution, intersecting branes, radius stabilization, KK phenomenology and bulk gauge bosons. ∗Lectures at the Theoretical Advanced Study Institute 2002, University of Colorado, Boulder, CO June 3-28, 2002. Contents 1 Introduction 2 2 Large Extra Dimensions 2 2.1 Matching the higher dimensional theory to the 4D effectivetheory..... 3 2.2 What is a brane and how to write an effective theory for it? . ....... 7 2.3 Coupling of SM fields to the various graviton components . ......... 11 2.4 Phenomenology with large extra dimensions . ...... 16 3 Various Models with Flat Extra Dimensions 21 3.1 Split fermions, proton decay and flavor hierarchy . ......... 21 3.2 Mediation of supersymmetry breaking via extra dimensions (gaugino mediation) 26 3.3 Symmetry breaking via orbifolds . .... 33 3.3.1 Breaking of the grand unified gauge group via orbifolds in SUSY GUT’s 35 3.3.2 Supersymmetry breaking via orbifolds . -
Photon Mixing in Universes with Large Extra–Dimensions
CORE Photon mixing in universes with large extra{dimensionsMetadata, citation and similar papers at core.ac.uk Provided by CERN Document Server C´edric Deffayet1 and Jean–Philippe Uzan1,2 (1) Laboratoire de Physique Th´eorique∗, Universit´e Paris XI, B^at. 210 F{91405 Orsay Cedex (France). (2) D´epartement de Physique Th´eorique, Universit´edeGen`eve, 24 quai E. Ansermet, CH{1211 Gen`eve 4 (Switzerland). (February 17, 2000) In presence of a magnetic field, photons can mix with any particle having a two{photon vertex. In theories with large compact extra{dimensions, there exists a hierachy of massive Kaluza{Klein gravitons that couple to any photon entering a magnetic field. We study this mixing and show that, in comparison with the four dimensional situation where the photon couples only to the massless graviton, the oscillation effect may be enhanced due to the existence of a large number of Kaluza{ Klein modes. We give the conditions for such an enhancement and then investigate the cosmological and astrophysical consequences of this phenomenon; we also discuss some laboratory experiments. Axions also couple to photons in the same way; we discuss the effect of the existence of bulk axions in universes with large extra{dimensions. The results can also be applied to neutrino physics with extra{dimensions. Preprint numbers: UGVA{DPT 99/10-1053, LPT{ORSAY 99/104 I. INTRODUCTION It is well known [1,2] that photons can be converted into gravitons by a magnetic field in a standard four dimensional spacetime. The propagation eigenstates are then mixtures of photon and graviton interaction eigenstates. -
Spacetime Geometry from Graviton Condensation: a New Perspective on Black Holes
Spacetime Geometry from Graviton Condensation: A new Perspective on Black Holes Sophia Zielinski née Müller München 2015 Spacetime Geometry from Graviton Condensation: A new Perspective on Black Holes Sophia Zielinski née Müller Dissertation an der Fakultät für Physik der Ludwig–Maximilians–Universität München vorgelegt von Sophia Zielinski geb. Müller aus Stuttgart München, den 18. Dezember 2015 Erstgutachter: Prof. Dr. Stefan Hofmann Zweitgutachter: Prof. Dr. Georgi Dvali Tag der mündlichen Prüfung: 13. April 2016 Contents Zusammenfassung ix Abstract xi Introduction 1 Naturalness problems . .1 The hierarchy problem . .1 The strong CP problem . .2 The cosmological constant problem . .3 Problems of gravity ... .3 ... in the UV . .4 ... in the IR and in general . .5 Outline . .7 I The classical description of spacetime geometry 9 1 The problem of singularities 11 1.1 Singularities in GR vs. other gauge theories . 11 1.2 Defining spacetime singularities . 12 1.3 On the singularity theorems . 13 1.3.1 Energy conditions and the Raychaudhuri equation . 13 1.3.2 Causality conditions . 15 1.3.3 Initial and boundary conditions . 16 1.3.4 Outlining the proof of the Hawking-Penrose theorem . 16 1.3.5 Discussion on the Hawking-Penrose theorem . 17 1.4 Limitations of singularity forecasts . 17 2 Towards a quantum theoretical probing of classical black holes 19 2.1 Defining quantum mechanical singularities . 19 2.1.1 Checking for quantum mechanical singularities in an example spacetime . 21 2.2 Extending the singularity analysis to quantum field theory . 22 2.2.1 Schrödinger representation of quantum field theory . 23 2.2.2 Quantum field probes of black hole singularities . -
Abdus Salam United Nations Educational, Scientific and Cultural International XA0101583 Organization Centre
the 1(72001/34 abdus salam united nations educational, scientific and cultural international XA0101583 organization centre international atomic energy agency for theoretical physics NEW DIMENSIONS NEW HOPES Utpal Sarkar Available at: http://www.ictp.trieste.it/-pub-off IC/2001/34 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS NEW DIMENSIONS NEW HOPES Utpal Sarkar1 Physics Department, Visva Bharati University, Santiniketan 731235, India and The Abdus Salam Insternational Centre for Theoretical Physics, Trieste, Italy. Abstract We live in a four dimensional world. But the idea of unification of fundamental interactions lead us to higher dimensional theories. Recently a new theory with extra dimensions has emerged, where only gravity propagates in the extra dimension and all other interactions are confined in only four dimensions. This theory gives us many new hopes. In earlier theories unification of strong, weak and the electromagnetic forces was possible at around 1016 GeV in a grand unified theory (GUT) and it could get unified with gravity at around the Planck scale of 1019 GeV. With this new idea it is possible to bring down all unification scales within the reach of the next generation accelerators, i.e., around 104 GeV. MIRAMARE - TRIESTE May 2001 1 Regular Associate of the Abdus Salam ICTP. E-mail: [email protected] 1 Introduction In particle physics we try to find out what are the fundamental particles and how they interact. This is motivated from the belief that there must be some fundamental law that governs ev- erything. -
Large Extra Dimensions: Implications for the Strong CP Problem Keith R
Large Extra Dimensions: Implications for the Strong CP Problem Keith R. Dienes∗ Department of Physics, University of Arizona, Tucson Emilian Dudas† LPT, Bât. 210, Univ. Paris-Sud Tony Gherghetta‡ IPT, University of Lausanne In this talk, we summarize some of the novel effects that arise when the QCD axion is placed in the “bulk” of large extra spacetime dimensions. First, we find that the mass of the axion can become independent of the energy scale associated with the breaking of the Peccei–Quinn symmetry. This implies that the mass of the axion can be adjusted independently of its couplings to ordinary matter, a feature which is not possible in four dimensions and which may contribute to axion invisibility. Second, we discuss the new phenomenon of laboratory axion oscillations (analogous to neutrino os- cillations), and show that these oscillations cause laboratory axions to “decohere” extremely rapidly as a result of Kaluza–Klein mixing. This decoherence may also be a contributing factor to axion invisibility. Finally, we show that under certain circumstances, the presence of an infinite tower of Kaluza–Klein axion modes can significantly accelerate the dissipation of the energy associated with cosmological relic axion oscillations, thereby enabling the Peccei–Quinn symmetry-breaking scale to exceed the usual four-dimensional relic oscillation bounds. Together, these ideas provide new ways of obtaining an “invisible” axion within the context of higher-dimensional theories with large-radius compactifications. Over the past few years, the possibility that large extra spacetime dimensions might exist has received considerable attention. The main attraction of this idea is the observation that large extra dimensions have the potential to lower the fundamental energy scales of physics such as the Planck scale [1], the GUT scale [2], and the string scale [3]. -
SLAC-PUB3031 January 1983 (T) SPONTANEOUS CP VIOLATION IN
SLAC-PUB3031 January 1983 (T) - . SPONTANEOUS CP VIOLATION IN EXTENDED TECHNICOLOR MODELS WITH HORIZONTAL V(2)t @ U(~)R FLAVOR SYMMETRIES (II)* WILLIAM GOLDSTEIN Stanford Linear Accelerator Center Stanford University, Stanford, California S&l05 ABSTRACT -- The results presented in Part I of this paper are extended to-include previously neglected electro-weak degrees of freedom, and are illustrated in a toy model. A problem associated with colored technifermions is identified and discussed. Some hope is offered for the disappointing quark mass matrix obtained in Part I. Submitted to Nuclear Physics B * Work supported by the Department of Energy, contract DEAC03-76SF00515. 1. INTRODUCTION In a previous paper [l], hereafter referred to as I, we investigated sponta- neous CP violation in a class of extended technicolor (ETC) models [2,3,4,5]. We constructed the effective Hamiltonian generated by broken EZ’C interactions and minimized its contribution to the vacuum energy, as called for by Dashen’s - . Theorem [S]. As originally pointed out by Dashen, and more recently by Eichten, Lane and Preskill in the context of the EK’ program, this aligning of the chiral vacuum and Hamiltonian can lead to CP violation from an initially CP symmet- ric theory [7,8]. The ETC models analyzed in I were distinguished by the global flavor invari- ance of the color-technicolor forces: GF = n u(2)L @ u@)R (1) For-- these models, we found that, in general, the occurrence of spontaneous CP violation is tied to CP nonconservation in the strong interactions and, thus, - to an unacceptably large neutron electric dipole moment. -
Technicolor Evolution Elizabeth H
Technicolor Evolution Elizabeth H. Simmons∗ Physics Department, Boston University† This talk describes how modern theories of dynamical electroweak symmetry breaking have evolved from the original minimal QCD-like technicolor model in response to three key challenges: Rb, flavor-changing neutral currents, and weak isospin violation. 1. Introduction In order to understand the origin of mass, we must find both the cause of electroweak symme- try breaking, through which the W and Z bosons obtain mass, and the cause of flavor symmetry breaking, by which the quarks and leptons obtain their diverse masses and mixings. The Standard Higgs Model of particle physics, based on the gauge group SU(3)c × SU(2)W × U(1)Y accommo- dates both symmetry breakings by including a fundamental weak doublet of scalar (“Higgs”) + 2 = φ = † − 1 2 bosons φ φ0 with potential function V (φ) λ φ φ 2 v . However the Standard Model does not explain the dynamics responsible for the generation of mass. Furthermore, the scalar sector suffers from two serious problems. The scalar mass is unnaturally sensitive to the pres- ence of physics at any higher scale Λ (e.g. the Planck scale), as shown in fig. 1. This is known as the gauge hierarchy problem. In addition, if the scalar must provide a good description of physics up to arbitrarily high scale (i.e., be fundamental), the scalar’s self-coupling (λ) is driven to zero at finite energy scales as indicated in fig. 1. That is, the scalar field theory is free (or “trivial”). Then the scalar cannot fill its intended role: if λ = 0, the electroweak symmetry is not spontaneously broken. -
Investigation of Theories Beyond the Standard Model
Investigation of Theories beyond the Standard Model Sajid Ali1, Georg Bergner2, Henning Gerber1, Pietro Giudice1, Istvan´ Montvay3, Gernot Munster¨ 1, Stefano Piemonte4, and Philipp Scior1 1 Institut fur¨ Theoretische Physik, Universitat¨ Munster,¨ Wilhelm-Klemm-Str. 9, D-48149 Munster¨ E-mail: fsajid.ali, h.gerber, p.giudice, munsteg, [email protected] 2 Theoretisch-Physikalisches Institut, Universitat¨ Jena, Max-Wien-Platz 1, D-07743 Jena E-mail: [email protected] 3 Deutsches Elektronen-Synchrotron DESY, Notkestr. 85, D-22603 Hamburg E-mail: [email protected] 4 Fakultat¨ fur¨ Physik, Universitat¨ Regensburg, Universitatsstr.¨ 31, D-93053 Regensburg E-mail: [email protected] The fundamental constituents of matter and the forces between them are splendidly described by the Standard Model of elementary particle physics. Despite its great success, it will be superseded by more comprehensive theories that are able to include phenomena, which are not covered by the Standard Model. Among the attempts in this direction are supersymmetry and Technicolor models. We report about our non-perturbative investigations of the characteristic properties of such models by numerical simulations on high-performance computers. 1 Introduction The physics of elementary particles has a marvellous theoretical framework available, which is called the Standard Model. It accurately describes a vast number of phenom- ena and experiments. In the Standard Model the fundamental interactions among parti- cles are described in terms of gauge field theories, which are characterized by an infinite- dimensional group of symmetries. Despite its great success it is evident that the Standard Model does not offer a complete description of the fundamental constituents of matter and their interactions.