2015 Part III Lectures on 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. -
Consequences of Kaluza-Klein Covariance
CONSEQUENCES OF KALUZA-KLEIN COVARIANCE Paul S. Wesson Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada Space-Time-Matter Consortium, http://astro.uwaterloo.ca/~wesson PACs: 11.10Kk, 11.25Mj, 0.45-h, 04.20Cv, 98.80Es Key Words: Classical Mechanics, Quantum Mechanics, Gravity, Relativity, Higher Di- mensions Addresses: Mail to Waterloo above; email: [email protected] Abstract The group of coordinate transformations for 5D noncompact Kaluza-Klein theory is broader than the 4D group for Einstein’s general relativity. Therefore, a 4D quantity can take on different forms depending on the choice for the 5D coordinates. We illustrate this by deriving the physical consequences for several forms of the canonical metric, where the fifth coordinate is altered by a translation, an inversion and a change from spacelike to timelike. These cause, respectively, the 4D cosmological ‘constant’ to be- come dependent on the fifth coordinate, the rest mass of a test particle to become measured by its Compton wavelength, and the dynamics to become wave-mechanical with a small mass quantum. These consequences of 5D covariance – whether viewed as positive or negative – help to determine the viability of current attempts to unify gravity with the interactions of particles. 1. Introduction Covariance, or the ability to change coordinates while not affecting the validity of the equations, is an essential property of any modern field theory. It is one of the found- ing principles for Einstein’s theory of gravitation, general relativity. However, that theory is four-dimensional, whereas many theories which seek to unify gravitation with the interactions of particles use higher-dimensional spaces. -
Report of the Supersymmetry Theory Subgroup
Report of the Supersymmetry Theory Subgroup J. Amundson (Wisconsin), G. Anderson (FNAL), H. Baer (FSU), J. Bagger (Johns Hopkins), R.M. Barnett (LBNL), C.H. Chen (UC Davis), G. Cleaver (OSU), B. Dobrescu (BU), M. Drees (Wisconsin), J.F. Gunion (UC Davis), G.L. Kane (Michigan), B. Kayser (NSF), C. Kolda (IAS), J. Lykken (FNAL), S.P. Martin (Michigan), T. Moroi (LBNL), S. Mrenna (Argonne), M. Nojiri (KEK), D. Pierce (SLAC), X. Tata (Hawaii), S. Thomas (SLAC), J.D. Wells (SLAC), B. Wright (North Carolina), Y. Yamada (Wisconsin) ABSTRACT Spacetime supersymmetry appears to be a fundamental in- gredient of superstring theory. We provide a mini-guide to some of the possible manifesta- tions of weak-scale supersymmetry. For each of six scenarios These motivations say nothing about the scale at which nature we provide might be supersymmetric. Indeed, there are additional motiva- tions for weak-scale supersymmetry. a brief description of the theoretical underpinnings, Incorporation of supersymmetry into the SM leads to a so- the adjustable parameters, lution of the gauge hierarchy problem. Namely, quadratic divergences in loop corrections to the Higgs boson mass a qualitative description of the associated phenomenology at future colliders, will cancel between fermionic and bosonic loops. This mechanism works only if the superpartner particle masses comments on how to simulate each scenario with existing are roughly of order or less than the weak scale. event generators. There exists an experimental hint: the three gauge cou- plings can unify at the Grand Uni®cation scale if there ex- I. INTRODUCTION ist weak-scale supersymmetric particles, with a desert be- The Standard Model (SM) is a theory of spin- 1 matter tween the weak scale and the GUT scale. -
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. -
Off-Shell Interactions for Closed-String Tachyons
Preprint typeset in JHEP style - PAPER VERSION hep-th/0403238 KIAS-P04017 SLAC-PUB-10384 SU-ITP-04-11 TIFR-04-04 Off-Shell Interactions for Closed-String Tachyons Atish Dabholkarb,c,d, Ashik Iqubald and Joris Raeymaekersa aSchool of Physics, Korea Institute for Advanced Study, 207-43, Cheongryangri-Dong, Dongdaemun-Gu, Seoul 130-722, Korea bStanford Linear Accelerator Center, Stanford University, Stanford, CA 94025, USA cInstitute for Theoretical Physics, Department of Physics, Stanford University, Stanford, CA 94305, USA dDepartment of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India E-mail:[email protected], [email protected], [email protected] Abstract: Off-shell interactions for localized closed-string tachyons in C/ZN super- string backgrounds are analyzed and a conjecture for the effective height of the tachyon potential is elaborated. At large N, some of the relevant tachyons are nearly massless and their interactions can be deduced from the S-matrix. The cubic interactions be- tween these tachyons and the massless fields are computed in a closed form using orbifold CFT techniques. The cubic interaction between nearly-massless tachyons with different charges is shown to vanish and thus condensation of one tachyon does not source the others. It is shown that to leading order in N, the quartic contact in- teraction vanishes and the massless exchanges completely account for the four point scattering amplitude. This indicates that it is necessary to go beyond quartic inter- actions or to include other fields to test the conjecture for the height of the tachyon potential. Keywords: closed-string tachyons, orbifolds. -
Naturalness and New Approaches to the Hierarchy Problem
Naturalness and New Approaches to the Hierarchy Problem PiTP 2017 Nathaniel Craig Department of Physics, University of California, Santa Barbara, CA 93106 No warranty expressed or implied. This will eventually grow into a more polished public document, so please don't disseminate beyond the PiTP community, but please do enjoy. Suggestions, clarifications, and comments are welcome. Contents 1 Introduction 2 1.0.1 The proton mass . .3 1.0.2 Flavor hierarchies . .4 2 The Electroweak Hierarchy Problem 5 2.1 A toy model . .8 2.2 The naturalness strategy . 13 3 Old Hierarchy Solutions 16 3.1 Lowered cutoff . 16 3.2 Symmetries . 17 3.2.1 Supersymmetry . 17 3.2.2 Global symmetry . 22 3.3 Vacuum selection . 26 4 New Hierarchy Solutions 28 4.1 Twin Higgs / Neutral naturalness . 28 4.2 Relaxion . 31 4.2.1 QCD/QCD0 Relaxion . 31 4.2.2 Interactive Relaxion . 37 4.3 NNaturalness . 39 5 Rampant Speculation 42 5.1 UV/IR mixing . 42 6 Conclusion 45 1 1 Introduction What are the natural sizes of parameters in a quantum field theory? The original notion is the result of an aggregation of different ideas, starting with Dirac's Large Numbers Hypothesis (\Any two of the very large dimensionless numbers occurring in Nature are connected by a simple mathematical relation, in which the coefficients are of the order of magnitude unity" [1]), which was not quantum in nature, to Gell- Mann's Totalitarian Principle (\Anything that is not compulsory is forbidden." [2]), to refinements by Wilson and 't Hooft in more modern language. -
UC Berkeley UC Berkeley Electronic Theses and Dissertations
UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Discoverable Matter: an Optimist’s View of Dark Matter and How to Find It Permalink https://escholarship.org/uc/item/2sv8b4x5 Author Mcgehee Jr., Robert Stephen Publication Date 2020 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Discoverable Matter: an Optimist’s View of Dark Matter and How to Find It by Robert Stephen Mcgehee Jr. A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate Division of the University of California, Berkeley Committee in charge: Professor Hitoshi Murayama, Chair Professor Alexander Givental Professor Yasunori Nomura Summer 2020 Discoverable Matter: an Optimist’s View of Dark Matter and How to Find It Copyright 2020 by Robert Stephen Mcgehee Jr. 1 Abstract Discoverable Matter: an Optimist’s View of Dark Matter and How to Find It by Robert Stephen Mcgehee Jr. Doctor of Philosophy in Physics University of California, Berkeley Professor Hitoshi Murayama, Chair An abundance of evidence from diverse cosmological times and scales demonstrates that 85% of the matter in the Universe is comprised of nonluminous, non-baryonic dark matter. Discovering its fundamental nature has become one of the greatest outstanding problems in modern science. Other persistent problems in physics have lingered for decades, among them the electroweak hierarchy and origin of the baryon asymmetry. Little is known about the solutions to these problems except that they must lie beyond the Standard Model. The first half of this dissertation explores dark matter models motivated by their solution to not only the dark matter conundrum but other issues such as electroweak naturalness and baryon asymmetry. -
UV Behavior of Half-Maximal Supergravity Theories
UV behavior of half-maximal supergravity theories. Piotr Tourkine, Quantum Gravity in Paris 2013, LPT Orsay In collaboration with Pierre Vanhove, based on 1202.3692, 1208.1255 Understand the pertubative structure of supergravity theories. ● Supergravities are theories of gravity with local supersymmetry. ● Those theories naturally arise in the low energy limit of superstring theory. ● String theory is then a UV completion for those and thus provides a good framework to study their UV behavior. → Maximal and half-maximal supergravities. Maximal supergravity ● Maximally extended supergravity: – Low energy limit of type IIA/B theory, – 32 real supercharges, unique (ungauged) – N=8 in d=4 ● Long standing problem to determine if maximal supergravity can be a consistent theory of quantum gravity in d=4. ● Current consensus on the subject : it is not UV finite, the first divergence could occur at the 7-loop order. ● Impressive progresses made during last 5 years in the field of scattering amplitudes computations. [Bern, Carrasco, Dixon, Dunbar, Johansson, Kosower, Perelstein, Rozowsky etc.] Half-maximal supergravity ● Half-maximal supergravity: – Heterotic string, but also type II strings on orbifolds – 16 real supercharges, – N=4 in d=4 ● Richer structure, and still a lot of SUSY so explicit computations are still possible. ● There are UV divergences in d=4, [Fischler 1979] at one loop for external matter states ● UV divergence in gravity amplitudes ? As we will see the divergence is expected to arise at the four loop order. String models that give half-maximal supergravity “(4,0)” susy “(0,4)” susy ● Type IIA/B string = Superstring ⊗ Superstring Torus compactification : preserves full (4,4) supersymmetry. -
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 . -
Non-Critical String Theory Formulation of Microtubule Dynamics And
ACT-09/95 CERN-TH.127/95 CTP-TAMU-24/95 ENSLAPP-A|-/95 hep-ph/9505401 Non-Critical String Theory Formulation of Microtubule Dynamics and Quantum Asp ects of Brain Function a; b;c N.E. Mavromatos and D.V. Nanop oulos a Lab oratoire de Physique Theorique ENSLAPP (URA 14-36 du CNRS, asso ciee a l' E.N.S de Lyon, et au LAPP (IN2P3-CNRS) d'Annecy-le-Vieux), Chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux Cedex, France. b Texas A & M University, College Station, TX 77843-424 2, USA and Astroparticle Physics Group, Houston Advanced Research Center (HARC), The Mitchell Campus, Wo o dlands, TX 77381, USA. c CERN, Theory Division, Geneva 23 Switzerland Abstract Microtubule (MT) networks, subneural paracrystalline cytosceletal structures, seem to play a fundamental role in the neurons. We cast here the complicated MT dynamics in processed by the SLAC/DESY Libraries on 30 May 1995. 〉 the form of a 1 + 1-dimensional non-critical string theory,thus enabling us to provide a consistent quantum treatment of MTs, including enviromental friction e ects. We suggest, thus, that the MTs are the microsites, in the brain, for the emergence of stable, macroscopic PostScript quantum coherent states, identi able with the preconscious states. Quantum space-time e ects, as describ ed by non-critical string theory, trigger then an organizedcol lapse of the coherent states down to a sp eci c or conscious state. The whole pro cess we estimate to take O (1 sec), in excellent agreement with a plethora of exp erimental/observational ndings.