Superstring Theory -- Have Oscillation Modes That Correspond to Massless Particles
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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. -
From Vibrating Strings to a Unified Theory of All Interactions
Barton Zwiebach From Vibrating Strings to a Unified Theory of All Interactions or the last twenty years, physicists have investigated F String Theory rather vigorously. The theory has revealed an unusual depth. As a result, despite much progress in our under- standing of its remarkable properties, basic features of the theory remain a mystery. This extended period of activity is, in fact, the second period of activity in string theory. When it was first discov- ered in the late 1960s, string theory attempted to describe strongly interacting particles. Along came Quantum Chromodynamics— a theoryof quarks and gluons—and despite their early promise, strings faded away. This time string theory is a credible candidate for a theoryof all interactions—a unified theoryof all forces and matter. The greatest complication that frustrated the search for such a unified theorywas the incompatibility between two pillars of twen- tieth century physics: Einstein’s General Theoryof Relativity and the principles of Quantum Mechanics. String theory appears to be 30 ) zwiebach mit physics annual 2004 the long-sought quantum mechani- cal 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. Nevertheless, intense work has demonstrated that string theory incorporates many features of the physical universe. It is reasonable to be very optimistic about the prospects of string theory. Perhaps one of the most impressive features of string theory is the appearance of gravity as one of the fluctuation modes of a closed string. Although it was not discov- ered exactly in this way, we can describe a logical path that leads to the discovery of gravity in string theory. -
Three Duality Symmetries Between Photons and Cosmic String Loops, and Macro and Micro Black Holes
Symmetry 2015, 7, 2134-2149; doi:10.3390/sym7042134 OPEN ACCESS symmetry ISSN 2073-8994 www.mdpi.com/journal/symmetry Article Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes David Jou 1;2;*, Michele Sciacca 1;3;4;* and Maria Stella Mongiovì 4;5 1 Departament de Física, Universitat Autònoma de Barcelona, Bellaterra 08193, Spain 2 Institut d’Estudis Catalans, Carme 47, Barcelona 08001, Spain 3 Dipartimento di Scienze Agrarie e Forestali, Università di Palermo, Viale delle Scienze, Palermo 90128, Italy 4 Istituto Nazionale di Alta Matematica, Roma 00185 , Italy 5 Dipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica (DICGIM), Università di Palermo, Viale delle Scienze, Palermo 90128, Italy; E-Mail: [email protected] * Authors to whom correspondence should be addressed; E-Mails: [email protected] (D.J.); [email protected] (M.S.); Tel.: +34-93-581-1658 (D.J.); +39-091-23897084 (M.S.). Academic Editor: Sergei Odintsov Received: 22 September 2015 / Accepted: 9 November 2015 / Published: 17 November 2015 Abstract: We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them through thermal equilibrium and stability between macro black holes and photon gas, and micro black holes and string loop gas, respectively. The possible cosmological consequences of these symmetries are discussed. Keywords: photons; cosmic string loops; black holes thermodynamics; duality symmetry 1. Introduction Thermal duality relates high-energy and low-energy states of corresponding dual systems in such a way that the thermal properties of a state of one of them at some temperature T are related to the properties of a state of the other system at temperature 1=T [1–6]. -
Florida Physics News University of Florida - Department of Physics Annual Alumni Newsletter 2005
Florida Physics News University of Florida - Department of Physics Annual Alumni Newsletter 2005 University of Florida - Department of Physics 1 Contents Chair’s Corner 2 Chair’s Corner UF Teacher/Scholar Award 3 American Physical Society - Three New Fellows 5 APS Keithley Award 5 November 2005 marks the third anniversary of Professors Earn Positions in National Societies 6 my term as department chair, and I can say that the Columbia Shuttle Accident Investigation 7 Student Government Award 8 past year has been the most exciting one (“exciting” Academy Induction 8 in the sense of the ancient Chinese curse, “May you Faculty Promotions 8 Post-Doc Awarded Fellowship from L’Oreal Corporation 8 live in exciting times”). Two significant events come to Research Scholar Award 8 mind: the record 2004 hurricane season, and the July Travel Awards 9 Undergraduate Physics Newsletter - In Review 10 2004 implementation of the new Enterprise Resource Albert Einstein Institut Rewards Two Students 12 Planning so�ware from PeopleSo�, designed to Physics Teacher of the Year 12 manage UF’s financial, payroll, and human resources 25th Brandt-Ritchie Workshop 12 TannerFest 12 activities. As you know, Florida was hammered 45th Sanibel Symposium 13 by four hurricanes during last year’s season, and Faculty Retirement 13 Faculty Selected Publications 14 Hurricanes Frances and Jeanne directly hit Gainesville Davis Productivity Award 16 in September 2004. Although ultimately the damage to Staff Retirement 16 Employee Excellence Awardees 16 UF was minimal, with downed trees, power outages, Undergraduate Honors 16 and minor flooding, it was nonetheless a stressful time Outreach Program 17 Celebrating New PhD’s 18 for the many faculty, staff, and students who were Awards Made Possible By Alumni Donations 18 affected by the storms. -
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..................... -
Massless Particles
UNIFYING GR WITH QUANTUM THEORY John H. Schwarz GR100 MARCH 11, 2016 1 OUTLINE I) What does unifying GR and quantum theory mean? Why should we do it? II) String theory: history and concepts III) Surprising discoveries IV) Conclusion 2 Fundamental physics The ultimate goal of particle physics is to achieve a unified understanding of fundamental forces and particles in terms of beautiful and compelling mathematical principles. A related goal, which I will not discuss, is to understand the origin and evolution of the Universe. These themes were pioneered by Einstein. It seems appropriate to reflect on them in this centennial year of his general theory of relativity. 3 Fundamental constants Special Relativity: The speed of light, denoted c, is the same for all observers. It appears in the famous equation E = mc2 . Quantum theory: Planck’s constant, denoted h, appears in the famous Heisenberg uncertainty principle and in the equation E = hf , where f denotes frequency. Gravity: Newton’s constant, denoted G, appears in the famous force equation F = GmM /r2 . 4 I) Unification We need to unify: The Standard Model (SM) -- a relativistic quantum theory that describes the strong nuclear, weak nuclear, and electromagnetic forces. This theory involves c and h but not G. and General Relativity (GR) -- Einstein’s theory of gravity, unlike Newton’s, is relativistic. However, it is still classical (i.e., not quantum). This means that it involves c and G but not h. 5 The Standard Model • The SM is an extremely successful theory of matter particles (quarks and leptons), force particles (photon, gluons, etc.), as well as a Higgs particle, discovered at the LHC in 2012. -
Fermilab Theory Group
Fermilab Theory Group Christopher T. Hill DOE Annual Program Review Fermilab, May 17, 2006 Scale of Effort(s) Program Review FY05 FY06 FY07 FY08 Particle Theory (SWF+M&S+G&V) $3,598 $3,531 $3,731 $3,899 Lattice $1,451 $2,782 $2,733 $3,035 The support for the Lattice gauge is increasing; some of the funds come from SciDAC, some from the core budget. Scientists (12) Associate Scientists (1) Research Associates (9) Bill Bardeen Thomas Becher (9/04) Mu-Chun Chen Marcela Carena Richard Hill Estia Eichten Jay Hubicz Keith Ellis Jim Laiho Walter Giele Olga Mena Christopher Hill Senior Guest Scientist(1) Enrico Lunghi Andreas Kronfeld Jose Santiago Boris Kayser Joe Lykken Peter Skands Paul Mackenzie Ruth van de Water Bogdan Dobrescu* Emeritus Scientist (1) Regular Users Stephen Parke Leon M. Lederman C. Albright (NIU) Chris Quigg S. Mrenna (Fermilab, Computing) Y. Keung (UIC) *Promoted, 10/01/05 S.P. Martin (NIU) Ulrich Baur (Buffalo) Departures: Associate Scientist Search: Ayres Freitas Zurich ETH Babis Anastasiou (offered and declined) Giulia Zanderighi CERN Uli Haisch Zurich ETH History of the Post-Docs, Associate Masataka Okamoto KEK Scientists and Frontier Fellows is Ulrich Nierste Karlsruhe (Professor) posted on the web: http://theory.fnal.gov/people/ellis/alumni.html New Postdoc Hires arrived Fall 2005: http://theory.fnal.gov/people/ellis/Assoc.html Mu-Chun Chen (from BNL),(*) http://theory.fnal.gov/people/ellis/frontier.html Richard Hill (from SLAC), Jay Hubicz (from Cornell) Enrico Lunghi (from ETH) Ruth van de Water (from Seattle) (*) just received Jr. Faculty offer from Irvine New Postdoc Hires to arrive Fall 2006: K. -
The Early Years of String Theory: a Personal Perspective
CALT-68-2657 THE EARLY YEARS OF STRING THEORY: A PERSONAL PERSPECTIVE John H. Schwarz California Institute of Technology Pasadena, CA 91125, USA Abstract arXiv:0708.1917v3 [hep-th] 3 Apr 2009 This article surveys some of the highlights in the development of string theory through the first superstring revolution in 1984. The emphasis is on topics in which the author was involved, especially the observation that critical string theories provide consistent quantum theories of gravity and the proposal to use string theory to construct a unified theory of all fundamental particles and forces. Based on a lecture presented on June 20, 2007 at the Galileo Galilei Institute 1 Introduction I am happy to have this opportunity to reminisce about the origins and development of string theory from 1962 (when I entered graduate school) through the first superstring revolution in 1984. Some of the topics were discussed previously in three papers that were written for various special events in 2000 [1, 2, 3]. Also, some of this material was reviewed in the 1985 reprint volumes [4], as well as the string theory textbooks [5, 6]. In presenting my experiences and impressions of this period, it is inevitable that my own contributions are emphasized. Some of the other early contributors to string theory have presented their recollections at the Galileo Galilei Institute meeting on “The Birth of String Theory” in May 2007. Since I was unable to attend that meeting, my talk was given at the GGI one month later. Taken together, the papers in this collection should -
STRING THEORY in the TWENTIETH CENTURY John H
STRING THEORY IN THE TWENTIETH CENTURY John H. Schwarz Strings 2016 { August 1, 2016 ABSTRACT String theory has been described as 21st century sci- ence, which was discovered in the 20th century. Most of you are too young to have experienced what happened. Therefore, I think it makes sense to summarize some of the highlights in this opening lecture. Since I only have 25 minutes, this cannot be a com- prehensive history. Important omitted topics include 2d CFT, string field theory, topological string theory, string phenomenology, and contributions to pure mathematics. Even so, I probably have too many slides. 1 1960 { 68: The analytic S matrix The goal was to construct the S matrix that describes hadronic scattering amplitudes by assuming • Unitarity and analyticity of the S matrix • Analyticity in angular momentum and Regge Pole The- ory • The bootstrap conjecture, which developed into Dual- ity (e.g., between s-channel and t-channel resonances) 2 The dual resonance model In 1968 Veneziano found an explicit realization of duality and Regge behavior in the narrow resonance approxima- tion: Γ(−α(s))Γ(−α(t)) A(s; t) = g2 ; Γ(−α(s) − α(t)) 0 α(s) = α(0) + α s: The motivation was phenomenological. Incredibly, this turned out to be a tree amplitude in a string theory! 3 Soon thereafter Virasoro proposed, as an alternative, g2 Γ(−α(s))Γ(−α(t))Γ(−α(u)) T = 2 2 2 ; −α(t)+α(u) −α(s)+α(u) −α(s)+α(t) Γ( 2 )Γ( 2 )Γ( 2 ) which has similar virtues. -
Superfluous Physics
Superfluous Physics Evan Berkowitz,1, ∗ William Donnelly,2 and Sylvia Zhu3, 4 (Scientists Undertaking Preposterous Etymological Research Collaboration) 1Institut f¨ur Kernphysik and Institute for Advanced Simulation, Forschungszentrum J¨ulich, 54245 J¨ulich Germany 2Perimeter Institute for Theoretical Physics, 31 Caroline St. N. Waterloo, ON, N2L 2Y5, Canada 3Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Callinstraße 38, 30167 Hannover Germany 4Leibniz Universit¨at Hannover, D-30167 Hannover, Germany (Dated: April 1, 2019) A superweapon of modern physics superscribes a wide superset of phenomena, ranging from supernumerary rainbows to superfluidity and even possible supermultiplets. I. INTRODUCTION The questions run too deep For such a simple man Won’t you please, Please tell me what we’ve learned? Supertramp, The Logical Song Supermassive black holes have nonzero supermass, the quantity that couples to N = 1 supergravity, while in theories with more supercharges one may have superdupermassive black holes, and so on. Just as the no-hair theorem tells us that non-rotating black holes can be described as massive and charged, the no-hair supertheorem tell us that non-rotating superheavy black holes can be described as supermassive and supercharged. String theory provides hope to understand how to go beyond the semiclassical limit to describe in detail if and how black holes preserve unitarity, while superstring theory provides hope to understand the unitarity of supermassive black holes. With the recent observation of normal black hole [1–5] and neutron star[6] mergers via gravitational waves by the super-sensitive Advanced LIGO and VIRGO detectors, it is not unreasonable to expect gravitational-wave detections of supernovae of collapsing superstars or violent supermassive black hole astrophysical phenomena are on the horizon or, if you’ll forgive the absurd pun, superhorizon. -
Introduction to Superstring Theory
Introduction to Superstring theory Carmen Nunez Instituto de Astronomia y Física del Espacio C.C. 67 - Sue. 28, 1428 Buenos Aires, Argentina and Physics Department, University of Buenos Aires [email protected] Abstract 1 Overview The bosonic string theory, despite all its beautiful features, has a number of short comings. The most obvious of these are the absence of fermions and the presence of tachyons in spacetime. The tachyon is not an actual physical inconsistency; it indicates at least that the calculations are being performed in an unstable vacuum state. More over, tachyon exchange contributes infrarred divergences in loop diagrams and these divergences make it hard to isolate the ultraviolet behaviour of the "unified quan tum theory" the bosonic string theory gives rise to and determine whether it is really satisfactory. Historically, the solution to the tachyon problem appeared with the solution to the other problem, the absence of fermions. The addition of a new ingredient, supersym- metry on the world-sheet, improves substantially the general picture. In 1977 Gliozzi, Scherk and Olive showed that it was possible to get a model with no tachyons and with equal masses and multiplicities for bosons and fermions. In 1980, Green and Schwarz proved that this model had spacetime supersymmetry. In the completely consisten- t tachyon free form of the superstring theory it was then possible to show that the one-loop diagrams were completely finite and free of ultraviolet divergences. While most workers on the subject believe that the finiteness will also hold to all orders of perturbation theory, complete and universally accepted proofs have not appeared so far. -
Introduction to Superstring Theory
Introduction to Superstring Theory Carmen N´u~nez IAFE (UBA-CONICET) & PHYSICS DEPT. (University of Buenos Aires) VI ICTP LASS 2015 Mexico, 26 October- 6 November 2015 . Programme Class 1: The classical fermionic string Class 2: The quantized fermionic string Class 3: Partition Function Class 4: Interactions . Outline Class 1: The classical fermionic string The action and its symmetries Gauge fixing and constraints Equations of motion and boundary conditions Oscillator expansions . The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V . If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? . The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V . If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. If there is some other stable vacuum, this is not an actual inconsistency. Why superstrings? The spectra of bosonic strings contain a tachyon ! it might indicate the vacuum has been incorrectly identified. The mass squared of a particle T is the quadratic term in the 2 @2V (T ) j − 4 ) action: M = @T 2 T =0 = α0 = we are expanding around a maximum of V .