Loop Quantisation of Supergravity Theories Schleifenquantisierung
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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. -
What Can We Learn from Shape Dynamics? International Loop Quantum Gravity Seminar
What can we learn from shape dynamics? International Loop Quantum Gravity Seminar Tim A. Koslowski University of New Brunswick, Fredericton, NB, Canada November 12, 2013 Tim A. Koslowski (UNB) What can we learn from shape dynamics? November 12, 2013 1 / 19 Outline 1 Motivation from 2+1 diemsnional qunatum gravity to consider conformal evolution as fundamental 2 Conformal evolution is different from spacetime (i.e. abandon spacetime) 3 Generic dynamical emergence of spacetime in the presence of matter (i.e. regain spacetime) Tim A. Koslowski (UNB) What can we learn from shape dynamics? November 12, 2013 2 / 19 Introduction and Motivation Tim A. Koslowski (UNB) What can we learn from shape dynamics? November 12, 2013 3 / 19 Motivation Canonical metric path integral in 2+1 (only known metric path integral) ab p necessary: 2+1 split and CMC gauge condition gabπ − t g = 0 R 2 ab R ab a pπ c i dtd x(_gabπ −S(N)−H(ξ)) Z = [dgab][dπ ][dN][dξ ]δ[ g − t]δ[F ] det[FP ]e R 2 A R A i dtd x(_τAp −Vo(τ;p;t)) = [dτA][dp ]e [Carlip: CQG 12 (1995) 2201, Seriu PRD 55 (1997) 781] where: τA are Teichm¨ullerparameters, Vo(τ; p; t) denotes on-shell volume, which depends explicitly on time t ) QM on Teichm¨ullerspace, phys. Hamilt. Vo(τ; p; t) [Moncrief: JMP 30 (1989) 2907] Fradkin-Vilkovisky theorem: [cf. Henneaux/Teitelboim: \Quantization of Gauge Systems"] \Partition function depends on gauge fixing cond. only through the gauge equivalence class of gauge fixing conditions." for a discussion and some examples of non-equivalence [see Govaerts, Scholtz: J.Phys. -
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. -
Shape Dynamics
Shape Dynamics Tim A. Koslowski Abstract Barbour’s formulation of Mach’s principle requires a theory of gravity to implement local relativity of clocks, local relativity of rods and spatial covariance. It turns out that relativity of clocks and rods are mutually exclusive. General Relativity implements local relativity of clocks and spatial covariance, but not local relativity of rods. It is the purpose of this contribution to show how Shape Dynamics, a theory that is locally equivalent to General Relativity, implements local relativity of rods and spatial covariance and how a BRST formulation, which I call Doubly General Relativity, implements all of Barbour’s principles. 1 Introduction A reflection on Mach’s principle lead Barbour to postulate that rods and spatial frames of reference should be locally determined by a procedure that he calls “best matching,” while clocks should be locally determined by what he calls “objective change.” (For more, see [1].) More concretely, Barbour’s principles postulate lo- cal time reparametrization invariance, local spatial conformal invariance and spatial covariance. The best matching algorithm for spatial covariance and local spatial conformal invariance turns out to be equivalent to the imposition of linear diffeo- morphism and conformal constraints Z Z 3 ab 3 H(x) = d xp (Lx g)ab; C(r) = d xr p; (1) S S Tim A. Koslowski Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, Canada New address: Department of Mathematics and Statistics, University of New Brunswick Fredericton, New Brunswick E3B 5A3, Canada e-mail: [email protected] 1 2 Tim A. -
On the Axioms of Causal Set Theory
On the Axioms of Causal Set Theory Benjamin F. Dribus Louisiana State University [email protected] November 8, 2013 Abstract Causal set theory is a promising attempt to model fundamental spacetime structure in a discrete order-theoretic context via sets equipped with special binary relations, called causal sets. The el- ements of a causal set are taken to represent spacetime events, while its binary relation is taken to encode causal relations between pairs of events. Causal set theory was introduced in 1987 by Bombelli, Lee, Meyer, and Sorkin, motivated by results of Hawking and Malament relating the causal, conformal, and metric structures of relativistic spacetime, together with earlier work on discrete causal theory by Finkelstein, Myrheim, and 't Hooft. Sorkin has coined the phrase, \order plus number equals geometry," to summarize the causal set viewpoint regarding the roles of causal structure and discreteness in the emergence of spacetime geometry. This phrase represents a specific version of what I refer to as the causal metric hypothesis, which is the idea that the properties of the physical universe, and in particular, the metric properties of classical spacetime, arise from causal structure at the fundamental scale. Causal set theory may be expressed in terms of six axioms: the binary axiom, the measure axiom, countability, transitivity, interval finiteness, and irreflexivity. The first three axioms, which fix the physical interpretation of a causal set, and restrict its \size," appear in the literature either implic- itly, or as part of the preliminary definition of a causal set. The last three axioms, which encode the essential mathematical structure of a causal set, appear in the literature as the irreflexive formula- tion of causal set theory. -
David Olive: His Life and Work
David Olive his life and work Edward Corrigan Department of Mathematics, University of York, YO10 5DD, UK Peter Goddard Institute for Advanced Study, Princeton, NJ 08540, USA St John's College, Cambridge, CB2 1TP, UK Abstract David Olive, who died in Barton, Cambridgeshire, on 7 November 2012, aged 75, was a theoretical physicist who made seminal contributions to the development of string theory and to our understanding of the structure of quantum field theory. In early work on S-matrix theory, he helped to provide the conceptual framework within which string theory was initially formulated. His work, with Gliozzi and Scherk, on supersymmetry in string theory made possible the whole idea of superstrings, now understood as the natural framework for string theory. Olive's pioneering insights about the duality between electric and magnetic objects in gauge theories were way ahead of their time; it took two decades before his bold and courageous duality conjectures began to be understood. Although somewhat quiet and reserved, he took delight in the company of others, generously sharing his emerging understanding of new ideas with students and colleagues. He was widely influential, not only through the depth and vision of his original work, but also because the clarity, simplicity and elegance of his expositions of new and difficult ideas and theories provided routes into emerging areas of research, both for students and for the theoretical physics community more generally. arXiv:2009.05849v1 [physics.hist-ph] 12 Sep 2020 [A version of section I Biography is to be published in the Biographical Memoirs of Fellows of the Royal Society.] I Biography Childhood David Olive was born on 16 April, 1937, somewhat prematurely, in a nursing home in Staines, near the family home in Scotts Avenue, Sunbury-on-Thames, Surrey. -
Annual Report 2013 NARODOWE CENTRUM BADAŃ JĄDROWYCH NATIONAL CENTRE for NUCLEAR RESEARCH
Annual Report 2013 NARODOWE CENTRUM BADAŃ JĄDROWYCH NATIONAL CENTRE FOR NUCLEAR RESEARCH ANNUAL REPORT 2013 PL-05-400 Otwock-Świerk, POLAND tel.: 048 22 718 00 01 fax: 048 22 779 34 81 e-mail: [email protected] http://www.ncbj.gov.pl Editors: N. Keeley K. Kurek Cover design: S. Mirski Secretarial work and layout: G. Swiboda ISSN 2299-2960 Annual Report 2013 3 CONTENTS FOREWORD ............................................................................................................................................................ 5 I. GENERAL INFORMATION ................................................................................................... 7 1. LOCATIONS ...................................................................................................................... 7 2. MANAGEMENT OF THE INSTITUTE ............................................................................ 7 3. SCIENTIFIC COUNCIL ..................................................................................................... 8 4. MAIN RESEARCH ACTIVITIES ................................................................................... 11 5. SCIENTIFIC STAFF OF THE INSTITUTE .................................................................... 13 6. VISITING SCIENTISTS .................................................................................................. 15 7. PARTICIPATION IN NATIONAL CONSORTIA AND SCIENTIFIC NETWORKS .. 23 8. DEGREES ........................................................................................................................ -
M-Theory Solutions and Intersecting D-Brane Systems
M-Theory Solutions and Intersecting D-Brane Systems A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy in the Department of Physics and Engineering Physics University of Saskatchewan Saskatoon By Rahim Oraji ©Rahim Oraji, December/2011. All rights reserved. Permission to Use In presenting this thesis in partial fulfilment of the requirements for a Postgrad- uate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this thesis in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my thesis work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this thesis or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis. Requests for permission to copy or to make other use of material in this thesis in whole or part should be addressed to: Head of the Department of Physics and Engineering Physics 116 Science Place University of Saskatchewan Saskatoon, Saskatchewan Canada S7N 5E2 i Abstract It is believed that fundamental M-theory in the low-energy limit can be described effectively by D=11 supergravity. -
M(Embrane)-Theory
Master of science thesis in physics M(embrane)-Theory Viktor Bengtsson Department of Theoretical Physics Chalmers University of Technology and GÄoteborg University Winter 2003 M(embrane)-Theory Viktor Bengtsson Department of Theoretical Physics Chalmers University of Technology and GÄoteborg University SE-412 96 GÄoteborg, Sweden Abstract We investigate the uses of membranes in theoretical physics. Starting with the bosonic membrane and the formulation of its dynamics we then move forward in time to the introduction of supersymmetry. Matrix theory is introduced and a full proof of the continuous spectrum of the supermembrane is given. After this we deal with various concepts in M-theory (BPS-states, Matrix Theory, torodial compacti¯cations etc.) that are of special importance when motivating the algebraic approach to M-theoretic caluclations. This approach is then dealt with by ¯rst reviewing the prototypical example of the Type IIB R4 amplitude and then the various issues of microscopic derivations of the corresponding results through ¯rst-principle computations in M-theory. This leads us to the mathematics of automorphic forms and the main result of this thesis, a calculation of the p-adic spherical vector in a minimal representation of SO(4; 4; Z) Acknowledgments I would like to extend the warmest thanks to my supervisor Prof. Bengt E.W. Nilsson for his unwavering patience with me during the last year. Many thanks also to my friend and collaborator Dr. Hegarty. I am most grateful to Dr. Anders Wall and the Wall Foundation for funding during the last year. I would like to thank Prof. Seif Randjbar-Daemi and the ICTP, Trieste, for their hospitality during this summer as well as Dr. -
Does Time Differ from Change? Philosophical Appraisal of the Problem of Time in Quantum Gravity and in Physics
Studies in History and Philosophy of Modern Physics 52 (2015) 48–54 Contents lists available at ScienceDirect Studies in History and Philosophy of Modern Physics journal homepage: www.elsevier.com/locate/shpsb Does time differ from change? Philosophical appraisal of the problem of time in quantum gravity and in physics Alexis de Saint-Ours Université Paris Diderot – CNRS, Laboratoire SPHERE, UMR 7219, Bâtiment Condorcet, case 7093, 5 rue Thomas Mann, 75205 Paris cedex 13, France article info abstract Article history: After reviewing the problem of time in Quantum Gravity, I compare from a philosophical perspective, Received 16 December 2013 both Carlo Rovelli's and Julian Barbour's (before Shape Dynamics) understanding of time in Quantum Received in revised form Gravity and in dynamics in general, trying to show that those two relational understandings of time 10 March 2015 differ. Rovelli argues that there is change without time and that time can be abstracted from any change Accepted 15 March 2015 whereas Barbour claims that some motions are better than others for constituting duration standards Available online 27 October 2015 To my father and that time is to be abstracted from all change in the universe. I conclude by a few remarks on Bergson's criticism of physics in the light of those debates trying to show that both Rovelli and Barbour Keywords: give surrationalist (as Bachelard understood it) answers to the critique of spatialized time in Physics. Time & 2015 Elsevier Ltd. All rights reserved. Change Barbour Rovelli Bergson Lautman When citing this paper, please use the full journal title Studies in History and Philosophy of Modern Physics 1. -
Introduction to Supergravity
Introduction to Supergravity Lectures presented by Henning Samtleben at the 13th Saalburg School on Fundamentals and New Methods in Theoretical Physics, September 3 { 14, 2007 typed by Martin Ammon and Cornelius Schmidt-Colinet ||| 1 Contents 1 Introduction 3 2 N = 1 supergravity in D = 4 dimensions 4 2.1 General aspects . 4 2.2 Gauging a global symmetry . 5 2.3 The vielbein formalism . 6 2.4 The Palatini action . 9 2.5 The supersymmetric action . 9 2.6 Results . 14 3 Extended supergravity in D = 4 dimensions 16 3.1 Matter couplings in N = 1 supergravity . 16 3.2 Extended supergravity in D = 4 dimensions . 17 4 Extended supergravity in higher Dimensions 18 4.1 Spinors in higher dimensions . 18 4.2 Eleven-dimensional supergravity . 20 4.3 Kaluza-Klein supergravity . 22 4.4 N = 8 supergravity in D = 4 dimensions . 26 A Variation of the Palatini action 27 2 1 Introduction There are several reasons to consider the combination of supersymmetry and gravitation. The foremost is that if supersymmetry turns out to be realized at all in nature, then it must eventually appear in the context of gravity. As is characteristic for supersymmetry, its presence is likely to improve the quantum behavior of the theory, particularly interesting in the context of gravity, a notoriously non-renormalizable theory. Indeed, in supergravity divergences are typically delayed to higher loop orders, and to date it is still not ruled out that the maximally supersymmetric extension of four-dimensional Einstein gravity might eventually be a finite theory of quantum gravity | only recently very tempting indications in this direction have been unvealed. -
What Is Time in Some Modern Physics Theories: Interpretation Problems
Ivan A. Karpenko WHAT IS TIME IN SOME MODERN PHYSICS THEORIES: INTERPRETATION PROBLEMS BASIC RESEARCH PROGRAM WORKING PAPERS SERIES: HUMANITIES WP BRP 124/HUM/2016 This Working Paper is an output of a research project implemented at the National Research University Higher School of Economics (HSE). Any opinions or claims contained in this Working Paper do not necessarily reflect the views of HSE. Ivan A. Karpenko1 WHAT IS TIME IN SOME MODERN PHYSICS THEORIES: INTERPRETATION PROBLEMS2 The article deals with the problem of time in the context of several theories of modern physics. This fundamental concept inevitably arises in physical theories, but so far there is no adequate description of it in the philosophy of science. In the theory of relativity, quantum field theory, Standard Model of particle physics, theory of loop quantum gravity, superstring theory and other most recent theories the idea of time is shown explicitly or not. Sometimes, such as in the special theory of relativity, it plays a significant role and sometimes it does not. But anyway it exists and is implied by the content of the theory, which in some cases directly includes its mathematical tools. Fundamental difference of space-time processes in microcosm and macrocosm is of particular importance for solving the problem. In this regard, a need to understand the time in the way it appears in modern physics, to describe it in the language of philosophy arises (satisfactory for time description mathematical tools also do not exist). This will give an opportunity to get closer to the answer on question of time characteristics.