Classical String Theory
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Chaos, Scaling and Existence of a Continuum Limit in Classical Non-Abelian Lattice Gauge Theory
LA-UR- 9 6 " 4 43"6" Los Alamos National Laboratory is operated by the University of Caiifomia for the United States Department of Energy under contract W-7405-ENG-36 TITLE: CHAOS, SCALING AND EXISTENCE OF A CONTINUUM Q&TJ LIMIT IN CLASSICAL NON-ABELIAN LATTICE GAUGE THEORY AUTHOR(S): Holger Nielsen, Niels Bohr Institute Hans Rugh, Universty of Warwick Svend Rugh, T-6 SUBMITTED TO: 28TH INTERNATIONAL CONFERENCE ON HIGH ENERGY PHYSICS, WARSAW POLAND, JULY 1996 By acceptance of this article, the publisher recognizes that the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or to allow others to do so, for U.S. Government purposes. The Los Alamos National Laboratory requests that the publisher identify this article as work performed under the auspices of the U.S. Department of Energy. Los Alamos National Laboratory L< Los Alamos, New Mexico 87545 FORM NO. 836 R4 ST. NO. 2629 5/81 DISTRIBUTION OF THIS DOCUMENT IS UNLIMITED DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. -
Lectures on D-Branes
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server CPHT/CL-615-0698 hep-th/9806199 Lectures on D-branes Constantin P. Bachas1 Centre de Physique Th´eorique, Ecole Polytechnique 91128 Palaiseau, FRANCE [email protected] ABSTRACT This is an introduction to the physics of D-branes. Topics cov- ered include Polchinski’s original calculation, a critical assessment of some duality checks, D-brane scattering, and effective worldvol- ume actions. Based on lectures given in 1997 at the Isaac Newton Institute, Cambridge, at the Trieste Spring School on String The- ory, and at the 31rst International Symposium Ahrenshoop in Buckow. June 1998 1Address after Sept. 1: Laboratoire de Physique Th´eorique, Ecole Normale Sup´erieure, 24 rue Lhomond, 75231 Paris, FRANCE, email : [email protected] Lectures on D-branes Constantin Bachas 1 Foreword Referring in his ‘Republic’ to stereography – the study of solid forms – Plato was saying : ... for even now, neglected and curtailed as it is, not only by the many but even by professed students, who can suggest no use for it, never- theless in the face of all these obstacles it makes progress on account of its elegance, and it would not be astonishing if it were unravelled. 2 Two and a half millenia later, much of this could have been said for string theory. The subject has progressed over the years by leaps and bounds, despite periods of neglect and (understandable) criticism for lack of direct experimental in- put. To be sure, the construction and key ingredients of the theory – gravity, gauge invariance, chirality – have a firm empirical basis, yet what has often catalyzed progress is the power and elegance of the underlying ideas, which look (at least a posteriori) inevitable. -
Pos(CORFU2019)049 ∗ -Ray Excess
Several degenerate vacua and a model for Dark Matter in the pure Standard Model PoS(CORFU2019)049 Holger Bech Nielsen∗ Niels Bohr Institute, Blegdamsvej 15 -21, Copenhagen E-mail: [email protected] Colin D. Froggatt Glasgow University E-mail: [email protected] We return to a model of ours for what the dark matter can be with the property that it is compatible with the Standard Model alone. The only genuine new physics is a principle imposing restrictions on the parameters/couplings in the Standard Model. They are required to lead to several vacua being degenerate in energy density with each other. We especially look for some of the signals from the dark matter, which are not just gravitational: The 3.55 keV X-ray radiation, the positron excess and further g-ray excess. The picture of ours for dark matter has it being cm-size pearls of 100000 ton mass in order of magnitude. Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019) 31 August - 25 September 2019 Corfu, Greece ∗Speaker. ⃝c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). http://pos.sissa.it/ Dark matter, pure S.M. Holger Bech Nielsen 1. Introduction Several degenerate vacua and a model for Dark Matter in the pure Standard Model We believe in the pure Standard Model further up in energy than most physicists, except for see-saw neutrinos and the baryon number excess for which we accept the need for new physics: • No new fundamental particles, except see-saw neutrinos and possibly particles almost at the Planck scale; but we shall not talk about such high energies today. -
String Theory University of Cambridge Part III Mathematical Tripos
Preprint typeset in JHEP style - HYPER VERSION January 2009 String Theory University of Cambridge Part III Mathematical Tripos Dr David Tong Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 OWA, UK http://www.damtp.cam.ac.uk/user/tong/string.html [email protected] –1– Recommended Books and Resources J. Polchinski, String Theory • This two volume work is the standard introduction to the subject. Our lectures will more or less follow the path laid down in volume one covering the bosonic string. The book contains explanations and descriptions of many details that have been deliberately (and, I suspect, at times inadvertently) swept under a very large rug in these lectures. Volume two covers the superstring. M. Green, J. Schwarz and E. Witten, Superstring Theory • Another two volume set. It is now over 20 years old and takes a slightly old-fashioned route through the subject, with no explicit mention of conformal field theory. How- ever, it does contain much good material and the explanations are uniformly excellent. Volume one is most relevant for these lectures. B. Zwiebach, A First Course in String Theory • This book grew out of a course given to undergraduates who had no previous exposure to general relativity or quantum field theory. It has wonderful pedagogical discussions of the basics of lightcone quantization. More surprisingly, it also has some very clear descriptions of several advanced topics, even though it misses out all the bits in between. P. Di Francesco, P. Mathieu and D. S´en´echal, Conformal Field Theory • This big yellow book is a↵ectionately known as the yellow pages. -
Arxiv:Hep-Th/0110227V1 24 Oct 2001 Elivrac Fpbae.Orcnieain a Eextended Be Can Considerations Branes
REMARKS ON WEYL INVARIANT P-BRANES AND Dp-BRANES J. A. Nieto∗ Facultad de Ciencias F´ısico-Matem´aticas de la Universidad Aut´onoma de Sinaloa, C.P. 80010, Culiac´an Sinaloa, M´exico Abstract A mechanism to find different Weyl invariant p-branes and Dp-branes actions is ex- plained. Our procedure clarifies the Weyl invariance for such systems. Besides, by consid- ering gravity-dilaton effective action in higher dimensions we also derive a Weyl invariant action for p-branes. We argue that this derivation provides a geometrical scenario for the arXiv:hep-th/0110227v1 24 Oct 2001 Weyl invariance of p-branes. Our considerations can be extended to the case of super-p- branes. Pacs numbers: 11.10.Kk, 04.50.+h, 12.60.-i October/2001 ∗[email protected] 1 1.- INTRODUCTION It is known that, in string theory, the Weyl invariance of the Polyakov action plays a central role [1]. In fact, in string theory subjects such as moduli space, Teichmuler space and critical dimensions, among many others, are consequences of the local diff x Weyl symmetry in the partition function associated to the Polyakov action. In the early eighties there was a general believe that the Weyl invariance was the key symmetry to distinguish string theory from other p-branes. However, in 1986 it was noticed that such an invariance may be also implemented to any p-brane and in particular to the 3-brane [2]. The formal relation between the Weyl invariance and p-branes was established two years later independently by a number of authors [3]. -
Pos(CORFU2016)050
F(750), We Miss You as a Bound State of 6 Top and 6 Antitop Quarks, Multiple Point Principle PoS(CORFU2016)050 Holger F. Bech Nielsen∗ y Niels Bohr Institute, Blegdamvej 15-21, DK 2100 Copenhagen Ø, Denmark D.L. Bennett Brooks Institute, Copenhagen, Denmark C.R. Das z BLTP, JINR, Dubna, Moscow, Russia C.D. Froggatt § Glasgow University, Glasgow, UK L.V. Laperashvili { ITEP, National Research Center “Kurchatov Institute”, Moscow, Russia We review our speculation, that in the pure Standard Model the exchange of Higgses, including also the ones “eaten by W ± and Z”, and of gluons together make a bound state of 6 top plus 6 anti top quarks bind so strongly that its mass gets down to about 1/3 of the mass of the collective mass 12 mt of the 12 constituent quarks. The true importance of this speculated bound state is that it makes it possible to uphold, even inside the Standard Mode, our proposal for what is really a new law of nature saying that there are several phases of empty space, vacua, all having very small energy densities (of the order of the present energy density in the universe). The reason suggested for believing in this new law called the “Multiple (Criticality) Point Principle” is, that estimating the mass of the speculated bound state using the “Multiple Point Principle” leads to two consistent mass-values; and they even agree with a crude bag-model like estimate of the mass of this bound state. Very unfortunately the statistical fluctuation so popular last year when interpreted as the digamma resonance F(750) turned out not to be a real resonance, because our estimated bound state mass is just around the mass of 750 GeV. -
D-Brane Actions and N = 2 Supergravity Solutions
D-Brane Actions and N =2Supergravity Solutions Thesis by Calin Ciocarlie In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2004 (Submitted May 20 , 2004) ii c 2004 Calin Ciocarlie All Rights Reserved iii Acknowledgements I would like to express my gratitude to the people who have taught me Physics throughout my education. My thesis advisor John Schwarz has given me insightful guidance and invaluable advice. I benefited a lot by collaborating with outstanding colleagues: Iosif Bena, Iouri Chepelev, Peter Lee, Jongwon Park. I have also bene- fited from interesting discussions with Vadim Borokhov, Jaume Gomis, Prof. Anton Kapustin, Tristan McLoughlin, Yuji Okawa, and Arkadas Ozakin. I am also thankful to my Physics teacher Violeta Grigorie who’s enthusiasm for Physics is contagious and to my family for constant support and encouragement in my academic pursuits. iv Abstract Among the most remarkable recent developments in string theory are the AdS/CFT duality, as proposed by Maldacena, and the emergence of noncommutative geometry. It has been known for some time that for a system of almost coincident D-branes the transverse displacements that represent the collective coordinates of the system become matrix-valued transforming in the adjoint representation of U(N). From a geometrical point of view this is rather surprising but, as we will see in Chapter 2, it is closely related to the noncommutative descriptions of D-branes. A consequence of the collective coordinates becoming matrix-valued is the ap- pearance of a “dielectric” effect in which D-branes can become polarized into higher- dimensional fuzzy D-branes. -
“Objects”, and Attempt Generalization to P-Adic Theory
Instructive Review of Novel SFT with Non-interacting consituents “objects”, and attempt Generalization to p-adic theory Holger Bech Nielsen∗ Niels Bohr Institute, Copenhagen University E-mail: [email protected] Masao Ninomiya Yukawa Institute for Theoretical Physics , Kyoto University, Kyoto 606-0105, Japan and Yuji Sugawara Lab., Science and Engineering , Department of Physics Sciences, Ritsumeikan university E-mail: [email protected] We have constructed a new formalism for describing a situation with several (dual) strings present at a time, a string field theory, by means of a constituent / a strings from objects picture similar to, but importantly different from the “bits” by Charles Thorn[1]. Our "objects" (essentially the bits) represent rather a making a lattice in the light cone variables on the string. The remarkable feature and simplicity of our formalism is, that the "objects" do NOT interact, basically just run or sit trivially fixed. Scattering is a fake in our formalism. This opens also up for hoping for generalizations inspired by hadrons with their partons all having Bjorken variable x = 0, and thus infinitely many constituents. The p-adic string is an example. Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019) 31 August - 25 September 2019 Corfu, Greece ∗Speaker. c Copyright owned by the author(s) under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ Generalizing Novel SFT Holger Bech Nielsen 1. Introduction We have worked since long on a formalism for a string field theory with the possibility of de- scribing an arbitrary number of strings, in other words a string field theory, which we called a Novel SFT.[3] Our “Novel SFT” has same spirit as the before ours developped string from bits reformu- lation of string theory by Charles Thorn [1]. -
Introductory Lectures on String Theory and the Ads/CFT Correspondence
AEI-2002-034 Introductory Lectures on String Theory and the AdS/CFT Correspondence Ari Pankiewicz and Stefan Theisen 1 Max-Planck-Institut f¨ur Gravitationsphysik, Albert-Einstein-Institut, Am M¨uhlenberg 1,D-14476 Golm, Germany Summary: The first lecture is of a qualitative nature. We explain the concept and the uses of duality in string theory and field theory. The prospects to understand QCD, the theory of the strong interactions, via string theory are discussed and we mention the AdS/CFT correspondence. In the remaining three lectures we introduce some of the tools which are necessary to understand many (but not all) of the issues which were raised in the first lecture. In the second lecture we give an elementary introduction to string theory, concentrating on those aspects which are necessary for understanding the AdS/CFT correspondence. We present both open and closed strings, introduce D-branes and determine the spectra of the type II string theories in ten dimensions. In lecture three we discuss brane solutions of the low energy effective actions, the type II supergravity theories. In the final lecture we compare the two brane pictures – D-branes and supergravity branes. This leads to the formulation of the Maldacena conjecture, or the AdS/CFT correspondence. We also give a brief introduction to the conformal group and AdS space. 1Based on lectures given in July 2001 at the Universidad Simon Bolivar and at the Summer School on ”Geometric and Topological Methods for Quantum Field Theory” in Villa de Leyva, Colombia. Lecture 1: Introduction There are two central open problems in theoretical high energy physics: the search for a quantum theory of gravity and • the solution of QCD at low energies. -
Calabi-Yau Compactification of Type II String Theories Sibasish Banerjee
Calabi-Yau compactification of type II string theories Sibasish Banerjee Composition of the thesis committee : Supervisor : Sergei Alexandrov, charg´ede Recherche, L2C CNRS, UMR-5221 Examiner : Boris Pioline, Professor LPTHE, Jussieu ; CERN PH-TH Examiner : Stefan Vandoren, Professor, ITP- Utrecht Chair : Andr´eNeveu, Professor Emeritus, L2C CNRS, UMR-5221 Examiner : Vasily Pestun, IHES,´ Bures-sur-yvette Examiner : Philippe Roche, Directeur de Recherche, IMAG, CNRS, Universit´ede Montpellier arXiv:1609.04454v1 [hep-th] 14 Sep 2016 Thesis defended at Laboratoire Charles Coulomb, Universit´ede Mont- pellier on 29th September, 2015. Contents 1 Some basic facts about string theory 1 1.1 A brief history of string theory . .2 1.2 Bosonic strings and Polyakov action . .3 1.2.1 World sheet point of view . .4 1.2.2 Weyl invariance . .4 1.3 Low energy limits primer . .6 1.4 Superstring theories . .7 1.4.1 M-theory and dualities . .9 1.5 String compactifications . 10 2 Compactification of type II string theories on Calabi-Yau three- folds and their moduli spaces 12 2.1 Calabi-Yau manifolds and their moduli spaces . 12 2.1.1 Complex structure moduli . 13 2.1.2 Kähler moduli . 14 2.2 Field content of type II supergravities in four dimensions . 15 2.2.1 Type IIA . 16 2.2.2 Type IIB . 17 2.3 Low energy effective actions . 18 2.4 Hypermultiplet moduli space . 20 2.4.1 Classical hypermultiplet metric . 20 2.4.2 Symmetries of the classical metric . 22 2.5 Qualitative nature of quantum correction . 24 2.6 Present status . -
What Comes Beyond the Standard Models Bled, July 11–19, 2016
i i “proc16” — 2016/12/12 — 10:17 — page I — #1 i i BLEJSKE DELAVNICE IZ FIZIKE LETNIK 17, STˇ . 2 BLED WORKSHOPS IN PHYSICS VOL. 17, NO. 2 ISSN 1580-4992 Proceedings to the 19th Workshop What Comes Beyond the Standard Models Bled, July 11–19, 2016 Edited by Norma Susana MankoˇcBorˇstnik Holger Bech Nielsen Dragan Lukman DMFA – ZALOZNIˇ STVOˇ LJUBLJANA, DECEMBER 2016 i i i i i i “proc16” — 2016/12/12 — 10:17 — page II — #2 i i The 19th Workshop What Comes Beyond the Standard Models, 11.– 19. July 2016, Bled was organized by Society of Mathematicians, Physicists and Astronomers of Slovenia and sponsored by Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana Society of Mathematicians, Physicists and Astronomers of Slovenia Beyond Semiconductor (MatjaˇzBreskvar) Scientific Committee John Ellis, CERN Roman Jackiw, MIT Masao Ninomiya, Okayama Institute for Quantum Physics Organizing Committee Norma Susana MankoˇcBorˇstnik Holger Bech Nielsen Maxim Yu. Khlopov The Members of the Organizing Committee of the International Workshop “What Comes Beyond the Standard Models”, Bled, Slovenia, state that the articles published in the Proceedings to the 19th Workshop “What Comes Beyond the Standard Models”, Bled, Slovenia are refereed at the Workshop in intense in-depth discussions. i i i i i i “proc16” — 2016/12/12 — 10:17 — page III — #3 i i Workshops organized at Bled . What Comes Beyond the Standard Models (June 29–July 9, 1998), Vol. 0 (1999) No. 1 (July 22–31, 1999) (July 17–31, 2000) (July 16–28, 2001), Vol. 2 (2001) No. 2 (July 14–25, 2002), Vol. -
A Symmetries of the QCD Phase Transition Using Chiral Lattice Fermions
The Chiral and U(1)A Symmetries of the QCD Phase Transition using Chiral Lattice Fermions Zhongjie Lin Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2014 ©2014 Zhongjie Lin All Rights Reserved Abstract The Chiral and U(1)A Symmetries of the QCD Phase Transition using Chiral Lattice Fermions Zhongjie Lin With regard to the nature of the finite-temperature QCD phase transition and the fate of the chiral and anomalous axial symmetries associated with it, we present in this thesis two parallel sets of investigations into the QCD phase transition region between 139 and 195 MeV. Both studies adopt the Iwasaki gauge action augmented with the dislocation suppression determinant ratio with 2+1 flavors of chiral fermions. This choice of lattice action accurately reproduces the SU(2)L × SU(2)R and U(1)A symmtries of the continuum. The first study simulates QCD thermodynamics on a line of constant physics that rep- resents 200 MeV pions and physical kaons using domain wall fermions (DWF) at three space-time volumes: 163 × 8, 243 × 8, and 323 × 8, where the largest volume varies in linear size between 5.6 fm (at T = 139 MeV) and 4.0 fm (at T = 195 MeV). The chiral condensates, connected and disconnected susceptibilities and the Dirac eigenvalue spectrum are reported and compared between different volumes as well as with the staggered results. We find a pseudo-critical temperature, Tc, of approximately 165 MeV and strong finite volume depen- dence below Tc.