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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. -
The Multiverse: Conjecture, Proof, and Science
The multiverse: conjecture, proof, and science George Ellis Talk at Nicolai Fest Golm 2012 Does the Multiverse Really Exist ? Scientific American: July 2011 1 The idea The idea of a multiverse -- an ensemble of universes or of universe domains – has received increasing attention in cosmology - separate places [Vilenkin, Linde, Guth] - separate times [Smolin, cyclic universes] - the Everett quantum multi-universe: other branches of the wavefunction [Deutsch] - the cosmic landscape of string theory, imbedded in a chaotic cosmology [Susskind] - totally disjoint [Sciama, Tegmark] 2 Our Cosmic Habitat Martin Rees Rees explores the notion that our universe is just a part of a vast ''multiverse,'' or ensemble of universes, in which most of the other universes are lifeless. What we call the laws of nature would then be no more than local bylaws, imposed in the aftermath of our own Big Bang. In this scenario, our cosmic habitat would be a special, possibly unique universe where the prevailing laws of physics allowed life to emerge. 3 Scientific American May 2003 issue COSMOLOGY “Parallel Universes: Not just a staple of science fiction, other universes are a direct implication of cosmological observations” By Max Tegmark 4 Brian Greene: The Hidden Reality Parallel Universes and The Deep Laws of the Cosmos 5 Varieties of Multiverse Brian Greene (The Hidden Reality) advocates nine different types of multiverse: 1. Invisible parts of our universe 2. Chaotic inflation 3. Brane worlds 4. Cyclic universes 5. Landscape of string theory 6. Branches of the Quantum mechanics wave function 7. Holographic projections 8. Computer simulations 9. All that can exist must exist – “grandest of all multiverses” They can’t all be true! – they conflict with each other. -
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. -
Modern Physics 436: Course Outline
Modern Physics 436: Course Outline 1. The book that I'm going to use for most part of the course will be • Modern Physics: J. Bernstein, P. Fishbane, S. Gasiorowicz (Prentice Hall) (It will be available at the Paragraphe Bookstore) 2. The course generally assumes that you are familiar with basics of integrations, differen- tiations, classical and quantum mechanics. Your pre-requisite are Phys 446, Phys 333. In this course I plan to cover the following topics: • Single particle atom: Basic review of Phys 446 • Multi-particle atoms: Molecules, molecular bondings • Statistical mechanics: Classical and quantum aspects, Maxwell-Boltzmann distribution, Fermi-Dirac distribution, Bose-Einstein distribution, Bose-Einstein condensation • Lasers: Induced radiations, coherent and squeezed states of light • Condensed matter Physics: Band structure, semiconductors, superconductivity, BCS theory, Hall effects (classical and quantum), Laughlin function • Nuclear Physics: Nuclear structure, nuclear interactions, nuclear models • Elementary Particle Physics: Quantum field theory (QFT), virtual particles, Feynman path-integrals, Feynman diagrams, Quantum electrodynamics (QED), particle zoo, weak interactions, leptons, hadrons, Quantum chromodynamics (QCD), quarks Wish-list: • General Relativity and Cosmology: Basic GTR, cosmological inflation, big-bang nucle- osynthesis • Superstring Theory: Very basic ideas, types of string theories, supersymmetry, super- gravity 3. Although I'll try to stick with one book, you're always advised to read other books for more details. A few other important books on the above topics are: • Quantum Mechanics: You may have already been using the book by David Griffiths. Another very good book is by Claude Cohen-Tannoudji, Bernard Diu and Frank Laloe. It comes in two volumes and does everything in full details. -
Classical String Theory
PROSEMINAR IN THEORETICAL PHYSICS Classical String Theory ETH ZÜRICH APRIL 28, 2013 written by: DAVID REUTTER Tutor: DR.KEWANG JIN Abstract The following report is based on my talk about classical string theory given at April 15, 2013 in the course of the proseminar ’conformal field theory and string theory’. In this report a short historical and theoretical introduction to string theory is given. This is fol- lowed by a discussion of the point particle action, leading to the postulation of the Nambu-Goto and Polyakov action for the classical bosonic string. The equations of motion from these actions are derived, simplified and generally solved. Subsequently the Virasoro modes appearing in the solution are discussed and their algebra under the Poisson bracket is examined. 1 Contents 1 Introduction 3 2 The Relativistic String4 2.1 The Action of a Classical Point Particle..........................4 2.2 The General p-Brane Action................................6 2.3 The Nambu Goto Action..................................7 2.4 The Polyakov Action....................................9 2.5 Symmetries of the Action.................................. 11 3 Wave Equation and Solutions 13 3.1 Conformal Gauge...................................... 13 3.2 Equations of Motion and Boundary Terms......................... 14 3.3 Light Cone Coordinates................................... 15 3.4 General Solution and Oscillator Expansion......................... 16 3.5 The Virasoro Constraints.................................. 19 3.6 The Witt Algebra in Classical String Theory........................ 22 2 1 Introduction In 1969 the physicists Yoichiro Nambu, Holger Bech Nielsen and Leonard Susskind proposed a model for the strong interaction between quarks, in which the quarks were connected by one-dimensional strings holding them together. However, this model - known as string theory - did not really succeded in de- scribing the interaction. -
Dear Brian Greene, When Friends Come to Visit at My House, They See
Dear Brian Greene, When friends come to visit at my house, they see warning signs on my door saying “High Voltage! Neutron Radiation!” This is because last spring, I took on the task of building a fusion reactor which is now operational and in a research phase. Thanks to the inspiration that I received from reading your book, The Elegant Universe, I have committed my life to a future in nuclear physics. Last year, I was searching for informational books on particle physics since this was an interest of mine; however, I found it difficult to find higher level materials that didn’t require college mathematics knowledge. The solution was your book, which I quickly read and have since been fascinated by the subject. The way that advanced topics are portrayed in a simple to understand and intriguing fashion make the book a brilliant piece of work that any aspiring physicist should read. I vividly recall two nights regarding my fascination with high energy physics. The first of those was the evening that I obtained a copy of The Elegant Universe after it was suggested to me as an excellent resource in string theory and quantum mechanics. I don’t think I ever went to bed that night while I devoured as much literature as I could. Within a week, I had completed the book and realized that my future was in this field. The other event that I recall was when I was searching for a science project online and stumbled upon fusor.net, a research consortium dedicated to amateur nuclear fusion. -
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]. -
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. -
At NYC Sci Fest, Asking 'What If We're Holograms?' 30 May 2010, by SAMANTHA GROSS , Associated Press Writer
At NYC sci fest, asking 'What if we're holograms?' 30 May 2010, By SAMANTHA GROSS , Associated Press Writer of the universe to scores of non-geniuses through his book "The Elegant Universe" and the PBS specials by the same name. The physicist founded the festival in 2008 with his wife, Tracy Day. In a way, they say, it's an extension of his work translating into layman's terms the fundamentals of string theory - the idea that the universe and its most fundamental forces could be best explained if everything around us were made up of minuscule, vibrating strings. Brian Greene, a string theorist known for bringing his Greene is not the only scientist working to show complex field of science to the masses, and Tracy Day, Americans the relevance of the field, and hoping to his wife and organizing partner behind World Science make it cooler for U.S. youth. Despite the recent Festival, pose in Times Square, New York, Wednesday murmurings about the era of "geek chic," many May 19, 2010. (AP Photo/Bebeto Matthews) teenagers still largely see science as a dorky pursuit, says Michio Kaku, a presenter at the festival and another string theorist who's built a career bringing his science to the public. (AP) -- Brian Greene works in a world where scientific reasoning rules all and imagination leads The numbers in the National Science Board's to the most unlikely truths. Greene and other yearly examination of science and engineering "string theorists" are exploring a possible scenario indicators paint a mixed picture for American in which people and the world around us are students. -
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. -
Brian Greene
BOOK REVIEW Staff undergraduate Editor-in-Chief BRIAN GREENE James Stankowicz physics The Fabric of the Cosmos: Space, Time, and the Texture of Reality Layout Director George CB Ling newsletter Brian Greene is a string theorist The final part of the book focuses Volume VI, Issue #1, September 2008 U P at Colombia University. His first on the experimental efforts (with Online Editor UP News Online: http://www.phys.ufl.edu/~upnews general public book, The Elegant many references to the LHC) Universe, was a Pulitzer Prize ongoing, the possibility of time Harold Rodriguez finalist, and served as the basis travel, and what might be waiting Production Manager as we delve ever further down LARGE HADRON who we are for a three hour PBS TV program Steven Hochman of the same name. into the fabric of reality. Assistant Editor COLLIDER UNVEILED! The Fabric of the Cosmos in some As The Fabric of the Cosmos is UP is a monthly undergraduate Alicia Swift It’s the world’s biggest and most in huge caves, track and analyze ways picks up where The Elegant written for the general public, physics newsletter sponsored ambitious scientific experiment exactly what happens. With more there are no mathematical Universe left off, but it is also a Staff Writers in human history. From revealing than 600 million collisions every by the University of Florida’s stand-alone book that doesn’t formulas in the main text, Arthur Ianuzzi what happened in the moments second, staggering volumes of chapter of the Society of Physics require any knowledge of The although the notes in the back of Bryce Bolin after the Big Bang, to probing the data are generated, hundreds of Elegant Universe. -
The Elegant Universe
The Elegant Universe Teacher’s Guide On the Web It’s the holy grail of physics—the search for the ultimate explanation of how the universe works. And in the past few years, excitement has grown among NOVA has developed a companion scientists in pursuit of a revolutionary approach to unify nature’s four Web site to accompany “The Elegant fundamental forces through a set of ideas known as superstring theory. NOVA Universe.” The site features interviews unravels this intriguing theory in its three-part series “The Elegant Universe,” with string theorists, online activities based on physicist Brian Greene’s best-selling book of the same name. to help clarify the concepts of this revolutionary theory, ways to view the The first episode introduces string theory, traces human understanding of the program online, and more. Find it at universe from Newton’s laws to quantum mechanics, and outlines the quest www.pbs.org/nova/elegant/ for and challenges of unification. The second episode traces the development of string theory and the Standard Model and details string theory’s potential to bridge the gap between quantum mechanics and the general theory of relativity. The final episode explores what the universe might be like if string theory is correct and discusses experimental avenues for testing the theory. Throughout the series, scientists who have made advances in the field share personal stories, enabling viewers to experience the thrills and frustrations of physicists’ search for the “theory of everything.” Program Host Brian Greene, a physicist who has made string theory widely accessible to public audiences, hosts NOVA’s three-part series “The Elegant Universe.” A professor of physics and mathematics at Columbia University in New York, Greene received his undergraduate degree from Harvard University and his doctorate from Oxford University, where he was a Rhodes Scholar.