Looking Back on the Story of the Space-Time Odyssey
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Supergravity and Its Legacy Prelude and the Play
Supergravity and its Legacy Prelude and the Play Sergio FERRARA (CERN – LNF INFN) Celebrating Supegravity at 40 CERN, June 24 2016 S. Ferrara - CERN, 2016 1 Supergravity as carved on the Iconic Wall at the «Simons Center for Geometry and Physics», Stony Brook S. Ferrara - CERN, 2016 2 Prelude S. Ferrara - CERN, 2016 3 In the early 1970s I was a staff member at the Frascati National Laboratories of CNEN (then the National Nuclear Energy Agency), and with my colleagues Aurelio Grillo and Giorgio Parisi we were investigating, under the leadership of Raoul Gatto (later Professor at the University of Geneva) the consequences of the application of “Conformal Invariance” to Quantum Field Theory (QFT), stimulated by the ongoing Experiments at SLAC where an unexpected Bjorken Scaling was observed in inclusive electron- proton Cross sections, which was suggesting a larger space-time symmetry in processes dominated by short distance physics. In parallel with Alexander Polyakov, at the time in the Soviet Union, we formulated in those days Conformal invariant Operator Product Expansions (OPE) and proposed the “Conformal Bootstrap” as a non-perturbative approach to QFT. S. Ferrara - CERN, 2016 4 Conformal Invariance, OPEs and Conformal Bootstrap has become again a fashionable subject in recent times, because of the introduction of efficient new methods to solve the “Bootstrap Equations” (Riccardo Rattazzi, Slava Rychkov, Erik Tonni, Alessandro Vichi), and mostly because of their role in the AdS/CFT correspondence. The latter, pioneered by Juan Maldacena, Edward Witten, Steve Gubser, Igor Klebanov and Polyakov, can be regarded, to some extent, as one of the great legacies of higher dimensional Supergravity. -
Varying Fundamental Constants and Particle Physics
Varying fundamental constants and particle physics Rikard Enberg Tanumoy Mandal Uppsala Seminar, 2017-04-06 Overview • The general idea • Old idea: Varying electromagnetic coupling • Particle physics à new scalar particles • Generalization to SU(3) × SU(2) × U(1) • Generalization to Yukawa couplings • Collider signatures All results in this talk are based on work with Ulf Danielsson, Gunnar Ingelman, Tanumoy Mandal: arXiv:1601.00624 (Nucl. Phys. B, in press) and a forthcoming paper 2 Free parameters of the SM Fundamental constant: a parameter that cannot be explained by the theory (even in principle) How many parameters are there in the Standard Model? • 19: Yukawas, gauge couplings, CKM, theta, Higgs • 26: If we include neutrino mixing and masses • 27: If we include the cosmological constant • 31–37: If we add cosmological standard model [See e.g. Tegmark et al., PRD 73 (2006) 023505] And then there are c, ħ, G, kB, etc. … Recommended reading: R.N. Cahn, Rev. Mod. Phys. 68 (1996) 951-960 M.J. Duff, arXiv:1412.2040 3 From Wikipedia, “Standard Model” Wikipedia, “Standard From 4 What are the fundamental constants and what are just units? • There’s a debate in the literature about what are the fundamental constants, and how many are there. [e.g. Duff, Okun. Veneziano, arXiv:physics/0110060] • Michael Duff in particular argues that only dimensionless constants are fundamental. Dimensionful constants are just unit conversions (Fathoms and nautical miles) speed of light = 1 lightyear/year • “Asking whether c has varied over cosmic history … is like asking whether the number of litres to the gallon has varied” [M.J. -
Twenty Years of the Weyl Anomaly
CTP-TAMU-06/93 Twenty Years of the Weyl Anomaly † M. J. Duff ‡ Center for Theoretical Physics Physics Department Texas A & M University College Station, Texas 77843 ABSTRACT In 1973 two Salam prot´eg´es (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor 2 gµν(x) Ω (x)gµν (x) displayed by classical massless field systems in interac- tion with→ gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic re- view. arXiv:hep-th/9308075v1 16 Aug 1993 CTP/TAMU-06/93 July 1993 †Talk given at the Salamfest, ICTP, Trieste, March 1993. ‡ Research supported in part by NSF Grant PHY-9106593. When all else fails, you can always tell the truth. Abdus Salam 1 Trieste and Oxford Twenty years ago, Derek Capper and I had embarked on our very first post- docs here in Trieste. We were two Salam students fresh from Imperial College filled with ideas about quantizing the gravitational field: a subject which at the time was pursued only by mad dogs and Englishmen. (My thesis title: Problems in the Classical and Quantum Theories of Gravitation was greeted with hoots of derision when I announced it at the Cargese Summer School en route to Trieste. The work originated with a bet between Abdus Salam and Hermann Bondi about whether you could generate the Schwarzschild solution using Feynman diagrams. You can (and I did) but I never found out if Bondi ever paid up.) Inspired by Salam, Capper and I decided to use the recently discovered dimensional regularization1 to calculate corrections to the graviton propaga- tor from closed loops of massless particles: vectors [1] and spinors [2], the former in collaboration with Leopold Halpern. -
Coordinate Space Approach to Double Copy Michael Duff Imperial College
Coordinate space approach to double copy Michael Duff Imperial College London based on [arXiv:1301.4176 arXiv:1309.0546 arXiv:1312.6523 arXiv:1402.4649 arXiv:1408.4434 arXiv:1602.08267 arXiv:1610.07192 arXiv:1707.03234 arXiv:1711.08476 arXiv:1807.02486 A. Anastasiou, L. Borsten, M. J. Duff, M. Hughes, A. Marrani, S. Nagy and M. Zoccali] Copenhagen August 2018 Basic idea Strong nuclear, Weak nuclear and Electromagnetic forces described by Yang-Mills gauge theory (non-abelian generalisation of Maxwell). Gluons, W, Z and photons have spin 1. Gravitational force described by Einstein’s general relativity. Gravitons have spin 2. But maybe (spin 2) = (spin 1)2. If so: 1) Do global gravitational symmetries follow from flat-space Yang-Mills symmetries? 2) Do local gravitational symmetries and Bianchi identities follow from flat-space Yang-Mills symmetries? 3) What about twin supergravities with same bosonic lagrangian but different fermions? 4) Are all supergravities Yang-Mills squared? Gravity as square of Yang-Mills A recurring theme in attempts to understand the quantum theory of gravity and appears in several different forms: Closed states from products of open states and KLT relations in string theory [Kawai, Lewellen, Tye:1985, Siegel:1988], On-shell D = 10 Type IIA and IIB supergravity representations from on-shell D = 10 super Yang-Mills representations [Green, Schwarz and Witten:1987], Vector theory of gravity [Svidzinsky 2009] Supergravity scattering amplitudes from those of super Yang-Mills in various dimensions, [Bern, Carrasco, Johanson:2008, 2010; Bern, Huang, Kiermaier, 2010: Bjerrum-Bohr, Damgaard, Monteiro, O’Connell 2012,Montiero, O’Connell, White 2011, 2014, Bianchi:2008, Elvang, Huang:2012, Cachazo:2013, Dolan:2013] Ambitwistor strings [Hodges:2011, Mason:2013, Geyer:2014] See talks by [Goldberger, Montiero, O’Connell] Gravity from Yang-Mills LOCAL SYMMETRIES: general covariance, local lorentz invariance, local supersymmetry, local p-form gauge invariance [ arXiv:1408.4434, Physica Scripta 90 (2015)] [ A. -
Einstein's Equations for Spin 2 Mass 0 from Noether's Converse Hilbertian
Einstein’s Equations for Spin 2 Mass 0 from Noether’s Converse Hilbertian Assertion October 4, 2016 J. Brian Pitts Faculty of Philosophy, University of Cambridge [email protected] forthcoming in Studies in History and Philosophy of Modern Physics Abstract An overlap between the general relativist and particle physicist views of Einstein gravity is uncovered. Noether’s 1918 paper developed Hilbert’s and Klein’s reflections on the conservation laws. Energy-momentum is just a term proportional to the field equations and a “curl” term with identically zero divergence. Noether proved a converse “Hilbertian assertion”: such “improper” conservation laws imply a generally covariant action. Later and independently, particle physicists derived the nonlinear Einstein equations as- suming the absence of negative-energy degrees of freedom (“ghosts”) for stability, along with universal coupling: all energy-momentum including gravity’s serves as a source for gravity. Those assumptions (all but) imply (for 0 graviton mass) that the energy-momentum is only a term proportional to the field equations and a symmetric curl, which implies the coalescence of the flat background geometry and the gravitational potential into an effective curved geometry. The flat metric, though useful in Rosenfeld’s stress-energy definition, disappears from the field equations. Thus the particle physics derivation uses a reinvented Noetherian converse Hilbertian assertion in Rosenfeld-tinged form. The Rosenfeld stress-energy is identically the canonical stress-energy plus a Belinfante curl and terms proportional to the field equations, so the flat metric is only a convenient mathematical trick without ontological commitment. Neither generalized relativity of motion, nor the identity of gravity and inertia, nor substantive general covariance is assumed. -
Guest Editorial: Truth, Beauty, and Supergravity Stanley Deser
Guest Editorial: Truth, beauty, and supergravity Stanley Deser Citation: American Journal of Physics 85, 809 (2017); doi: 10.1119/1.4994807 View online: http://dx.doi.org/10.1119/1.4994807 View Table of Contents: http://aapt.scitation.org/toc/ajp/85/11 Published by the American Association of Physics Teachers Articles you may be interested in Entanglement isn't just for spin American Journal of Physics 85, 812 (2017); 10.1119/1.5003808 Three new roads to the Planck scale American Journal of Physics 85, 865 (2017); 10.1119/1.4994804 A demonstration of decoherence for beginners American Journal of Physics 85, 870 (2017); 10.1119/1.5005526 The geometry of relativity American Journal of Physics 85, 683 (2017); 10.1119/1.4997027 The gravitational self-interaction of the Earth's tidal bulge American Journal of Physics 85, 663 (2017); 10.1119/1.4985124 John Stewart Bell and Twentieth-Century Physics: Vision and Integrity American Journal of Physics 85, 880 (2017); 10.1119/1.4983117 GUEST EDITORIAL Guest Editorial: Truth, beauty, and supergravity (Received 9 June 2017; accepted 28 June 2017) [http://dx.doi.org/10.1119/1.4994807] I begin with a warning: theoretical physics is an edifice Dirac equation governing the behavior of electrons—as well built over the centuries by some of mankind’s greatest minds, as all the other leptons and quarks, hence also our protons using ever more complicated and sophisticated concepts and and neutrons. Indeed, it is perhaps one of our three most mathematics to cover phenomena on scales billions of times beautiful equations, along with Maxwell’s and Einstein’s! It removed—in directions both bigger and smaller—from our came full-blown from the head of one of the true greats of human dimensions, where our simple intuition or primitive the last century, and instantly divided all particles into two language cannot pretend to have any validity. -
Personal Recollections of the Early Days Before and After the Birth of Supergravity
Personal recollections of the early days before and after the birth of Supergravity Peter van Nieuwenhuizen I March 29, 1976: Dan Freedman, Sergio Ferrara and I submit first paper on Supergravity to Physical Review D. I April 28: Stanley Deser and Bruno Zumino: elegant reformulation that stresses the role of torsion. I June 2, 2016 at 1:30pm: 5500 papers with Supergravity in the title have appeared, and 15000 dealing with supergravity. I Supergravity has I led to the AdS/CFT miracle, and I made breakthroughs in longstanding problems in mathematics. I Final role of supergravity? (is it a solution in search of a problem?) I 336 papers in supergravity with 126 collaborators I Now: many directions I can only observe in awe from the sidelines I will therefore tell you my early recollections and some anecdotes. I will end with a new research program that I am enthusiastic about. In 1972 I was a Joliot Curie fellow at Orsay (now the Ecole Normale) in Paris. Another postdoc (Andrew Rothery from England) showed me a little book on GR by Lawden.1 I was hooked. That year Deser gave lectures at Orsay on GR, and I went with him to Brandeis. In 1973, 't Hooft and Veltman applied their new covariant quantization methods and dimensional regularization to pure gravity, using the 't Hooft lemma (Gilkey) for 1-loop divergences and the background field formalism of Bryce DeWitt. They found that at one loop, pure gravity was finite: 1 2 2 ∆L ≈ αRµν + βR = 0 on-shell. But what about matter couplings? 1\An Introduction to Tensor Calculus and Relativity". -
Quantum Gravity: a Primer for Philosophers∗
Quantum Gravity: A Primer for Philosophers∗ Dean Rickles ‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared.1 I have also supplied references for those cases where I have omitted some important facts. -
Chern-Simons Terms As an Example of the Relations Between Mathematics and Physics
PUBLICATIONS MATHÉMATIQUES DE L’I.H.É.S. STANLEY DESER Chern-Simons terms as an example of the relations between mathematics and physics Publications mathématiques de l’I.H.É.S., tome S88 (1998), p. 47-51 <http://www.numdam.org/item?id=PMIHES_1998__S88__47_0> © Publications mathématiques de l’I.H.É.S., 1998, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions géné- rales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou im- pression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ CHERN-SIMONS TERMS AS AN EXAMPLE OF THE RELATIONS BETWEEN MATHEMATICS AND PHYSICS by STANLEY DESER The inevitability of Chern-Simons terms in constructing a variety of physical models, and the mathematical advances they in turn generate, illustrate the unexpected but profound interactions between the two disciplines. 1 begin with warmest greetings to the Institut des Hautes Études Scientifiques (IHÉS) on the occasion of its 40th birthday, and look forward to its successes in the years to come. My own association dates back to its early days in 1966-67 and it has continued fruitfully ever since. The IHÉS represents a unique synthesis between Mathematics and Physics, as empha- sized by this volume’s title. I propose to illustrate this synthesis through a particular set of examples, Chern-Simons "effects" in physics. -
String Theory and Our Relationship with Nature: the Convergence of Science, Curriculum Theory, and the Environment
Georgia Southern University Digital Commons@Georgia Southern Electronic Theses and Dissertations Graduate Studies, Jack N. Averitt College of Fall 2010 String Theory and Our Relationship with Nature: The Convergence of Science, Curriculum Theory, and the Environment Virginia Therese Bennett Follow this and additional works at: https://digitalcommons.georgiasouthern.edu/etd Recommended Citation Bennett, Virginia Therese, "String Theory and Our Relationship with Nature: The Convergence of Science, Curriculum Theory, and the Environment" (2010). Electronic Theses and Dissertations. 530. https://digitalcommons.georgiasouthern.edu/etd/530 This dissertation (open access) is brought to you for free and open access by the Graduate Studies, Jack N. Averitt College of at Digital Commons@Georgia Southern. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of Digital Commons@Georgia Southern. For more information, please contact [email protected]. STRING THEORY AND OUR RELATIONSHIP WITH NATURE: THE CONVERGENCE OF SCIENCE, CURRICULUM THEORY, AND THE ENVIRONMENT by VIRGINIA THERESE BENNETT (Under the Direction of John A. Weaver) ABSTRACT Curriculum Theory affords us the opportunity to examine education from a multitude of directions. This work takes advantage of that opportunity to explore the relationships between science, nature, and curriculum using string theory and our ideas about the environment as a backdrop. Both the energy and multiple possibilities created by strings and the rich history leading up to the theory help to illustrate the many opportunities we have to advance discussions in alternative ways of looking at science. By considering the multiple dimensions inherent in string theory as multiple pathways and interweaving metaphors from Deleuze and Guattari, Michel Serres, and Donna Haraway, our approach to environmental issues and environmental education allow us to include alternative ways of looking at the world. -
Constellations Education Resource Pack
CONSTELLATIONS BACKGROUND RESOURCES CONTENTS 1. About the Production 2. About the Writer 3. About the Play 4 & 5. Interview with Nick Payne 6. Interview with Lucy Cullingford 7. Practical Activities 8. Scene Study 9. Further Reading and Education at The Royal Court These resources are intended to give teachers and students a detailed insight into the creative process behind developing and staging Constellations. Through interviews, production notes and rehearsal techniques, they demonstrate how the writer, director and cast worked in collaboration to create the show. We aim to provide useful information and opportunities to help students discover the unique world of the play for themselves. DUKE OF YORKS THEATRE Constellations by Nick Payne Constellations had its premier at The Royal Court Jerwood Downstairs on Friday 13th January 2012 Constellations had its premier at The Duke of Yorks Theatre on Friday 9th November 2012 by Nick Payne Marianne Sally Hawkins Roland Rafe Spall Director Michael Longhurst Designer Tom Scutt Lighting Designer Lee Curran Composer Simon Slater Sound Designer David McSeveney Casting Director Amy Ball Assistant Director Sam Caird Production Manager Tariq Rifaat Movement Director Lucy Cullingford BSLBT Consultant Daryl Jackson Fight Director Kate Waters Stage Managers Rhiannon Harper, Bryan Paterson Stage Management Work Placement Amy Burkett Costume Supervisor Iona Kenrick WHAT THE CRITICS SAY: “Payne announced himself as a dramatist of rich humanity, vitality and promise. Here he makes a quantum leap with a -
Arxiv:1701.02422V1 [Hep-Th] 10 Jan 2017 Asnmes 46.M 11.15.Bt 04.60.-M, Numbers: PACS Operators
UCLA/16/TEP/103 SLAC–PUB–16905 Two-Loop Renormalization of Quantum Gravity Simplified Zvi Berna, Huan-Hang Chib, Lance Dixonb and Alex Edisona aMani L. Bhaumik Institute for Theoretical Physics Department of Physics and Astronomy University of California at Los Angeles Los Angeles, CA 90095, USA bSLAC National Accelerator Laboratory Stanford University Stanford, CA 94309, USA Abstract The coefficient of the dimensionally regularized two-loop R3 divergence of (nonsupersymmetric) gravity theories has recently been shown to change when non-dynamical three forms are added to the theory, or when a pseudo-scalar is replaced by the anti-symmetric two-form field to which it is dual. This phenomenon involves evanescent operators, whose matrix elements vanish in four dimensions, including the Gauss-Bonnet operator which is also connected to the trace anomaly. On the other hand, these effects appear to have no physical consequences in renormalized scattering arXiv:1701.02422v1 [hep-th] 10 Jan 2017 processes. In particular, the dependence of the two-loop four-graviton scattering amplitude on the renormalization scale is simple. In this paper, we explain this result for any minimally-coupled massless gravity theory with renormalizable matter interactions by using unitarity cuts in four dimensions and never invoking evanescent operators. PACS numbers: 04.60.-m, 11.15.Bt 1 I. INTRODUCTION Recent results show that the ultraviolet structure of gravity is much more interesting and subtle than might be anticipated from standard considerations. One example of a new ultraviolet surprise is the recent identification of “enhanced ultraviolet cancellations” in certain supergravity theories [1, 2], which are as yet unexplained by standard symme- tries [3].