STRINGS by Michael J
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
String Theory. Volume 1, Introduction to the Bosonic String
This page intentionally left blank String Theory, An Introduction to the Bosonic String The two volumes that comprise String Theory provide an up-to-date, comprehensive, and pedagogic introduction to string theory. Volume I, An Introduction to the Bosonic String, provides a thorough introduction to the bosonic string, based on the Polyakov path integral and conformal field theory. The first four chapters introduce the central ideas of string theory, the tools of conformal field theory and of the Polyakov path integral, and the covariant quantization of the string. The next three chapters treat string interactions: the general formalism, and detailed treatments of the tree-level and one loop amplitudes. Chapter eight covers toroidal compactification and many important aspects of string physics, such as T-duality and D-branes. Chapter nine treats higher-order amplitudes, including an analysis of the finiteness and unitarity, and various nonperturbative ideas. An appendix giving a short course on path integral methods is also included. Volume II, Superstring Theory and Beyond, begins with an introduction to supersym- metric string theories and goes on to a broad presentation of the important advances of recent years. The first three chapters introduce the type I, type II, and heterotic superstring theories and their interactions. The next two chapters present important recent discoveries about strongly coupled strings, beginning with a detailed treatment of D-branes and their dynamics, and covering string duality, M-theory, and black hole entropy. A following chapter collects many classic results in conformal field theory. The final four chapters are concerned with four-dimensional string theories, and have two goals: to show how some of the simplest string models connect with previous ideas for unifying the Standard Model; and to collect many important and beautiful general results on world-sheet and spacetime symmetries. -
Stephen Hawking: 'There Are No Black Holes' Notion of an 'Event Horizon', from Which Nothing Can Escape, Is Incompatible with Quantum Theory, Physicist Claims
NATURE | NEWS Stephen Hawking: 'There are no black holes' Notion of an 'event horizon', from which nothing can escape, is incompatible with quantum theory, physicist claims. Zeeya Merali 24 January 2014 Artist's impression VICTOR HABBICK VISIONS/SPL/Getty The defining characteristic of a black hole may have to give, if the two pillars of modern physics — general relativity and quantum theory — are both correct. Most physicists foolhardy enough to write a paper claiming that “there are no black holes” — at least not in the sense we usually imagine — would probably be dismissed as cranks. But when the call to redefine these cosmic crunchers comes from Stephen Hawking, it’s worth taking notice. In a paper posted online, the physicist, based at the University of Cambridge, UK, and one of the creators of modern black-hole theory, does away with the notion of an event horizon, the invisible boundary thought to shroud every black hole, beyond which nothing, not even light, can escape. In its stead, Hawking’s radical proposal is a much more benign “apparent horizon”, “There is no escape from which only temporarily holds matter and energy prisoner before eventually a black hole in classical releasing them, albeit in a more garbled form. theory, but quantum theory enables energy “There is no escape from a black hole in classical theory,” Hawking told Nature. Peter van den Berg/Photoshot and information to Quantum theory, however, “enables energy and information to escape from a escape.” black hole”. A full explanation of the process, the physicist admits, would require a theory that successfully merges gravity with the other fundamental forces of nature. -
Anomalies, Dualities, and Topology of D = 6 N = 1 Superstring Vacua
RU-96-16 NSF-ITP-96-21 CALT-68-2057 IASSNS-HEP-96/53 hep-th/9605184 Anomalies, Dualities, and Topology of D =6 N =1 Superstring Vacua Micha Berkooz,1 Robert G. Leigh,1 Joseph Polchinski,2 John H. Schwarz,3 Nathan Seiberg,1 and Edward Witten4 1Department of Physics, Rutgers University, Piscataway, NJ 08855-0849 2Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106-4030 3California Institute of Technology, Pasadena, CA 91125 4Institute for Advanced Study, Princeton, NJ 08540 Abstract We consider various aspects of compactifications of the Type I/heterotic Spin(32)/Z2 theory on K3. One family of such compactifications in- cludes the standard embedding of the spin connection in the gauge group, and is on the same moduli space as the compactification of arXiv:hep-th/9605184v1 25 May 1996 the heterotic E8 × E8 theory on K3 with instanton numbers (8,16). Another class, which includes an orbifold of the Type I theory re- cently constructed by Gimon and Polchinski and whose field theory limit involves some topological novelties, is on the moduli space of the heterotic E8 × E8 theory on K3 with instanton numbers (12,12). These connections between Spin(32)/Z2 and E8 × E8 models can be demonstrated by T duality, and permit a better understanding of non- perturbative gauge fields in the (12,12) model. In the transformation between Spin(32)/Z2 and E8 × E8 models, the strong/weak coupling duality of the (12,12) E8 × E8 model is mapped to T duality in the Type I theory. The gauge and gravitational anomalies in the Type I theory are canceled by an extension of the Green-Schwarz mechanism. -
Search for New Physics with Top Quark Pairs in the Fully Hadronic Final State at the ATLAS Experiment
Dissertation submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg, Germany for the degree of Doctor of Natural Sciences Put forward by Mathis Kolb born in Heidelberg Oral examination: November 21, 2018 Search for new physics with top quark pairs in the fully hadronic final state at the ATLAS experiment Referees: Prof. Dr. André Schöning Prof. Dr. Tilman Plehn Search for new physics with top quark pairs in the fully hadronic final state at the ATLAS experiment Fully hadronic final states containing top quark pairs (tt) are investigated using proton- proton collision data at a center of mass energy of 13 TeV recorded in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider at CERN. The bucket algorithm suppresses the large combinatorial background and is used to identify and reconstruct the tt system. It is applied in three analyses. A model independent search for new heavy particles decaying to tt using 36 fb−1 of data is presented. The analysis concentrates on an optimization of sensitivity at tt masses below 1:3 TeV. No excess from the Standard Model prediction is observed. Thus, upper limits at 95% C.L. are set on the production cross section times branching ratio of 0 benchmark signal models excluding e.g. a topcolor assisted technicolor ZTC2 in the mass range from 0:59 TeV to 1:25 TeV. The prospects of a search for the production of the Higgs boson in association with tt using 33 fb−1 of data recorded solely in 2016 are studied. -
Towards a String Dual of SYK Arxiv:2103.03187V1 [Hep-Th] 4 Mar
Towards A String Dual of SYK Akash Goel and Herman Verlinde Department of Physics, Princeton University, Princeton, NJ 08544, USA Abstract: We propose a paradigm for realizing the SYK model within string theory. Using the large N matrix description of c < 1 string theory, we show that the effective theory on a large number Q of FZZT D-branes in (p; 1) minimal string theory takes the form of the disorder averaged SYK model with J p interaction. The SYK fermions represent open strings between the FZZT branes and the ZZ branes that underly the matrix model. The continuum SYK dynamics arises upon taking the large Q limit. We observe several qualitative and quantitative links between the SYK model and (p; q) minimal string theory and propose that the two describe different phases of a single system. We comment on the dual string interpretation of double scaled SYK and on the relevance of our results to the recent discussion of the role of ensemble averaging in holography. arXiv:2103.03187v2 [hep-th] 24 Aug 2021 Contents 1 Introduction2 2 SYK from the Two Matrix Model4 2.1 FZZT-branes in the two matrix model4 2.2 Kontsevich matrix model from FZZT branes6 2.3 SYK matrix model from FZZT branes7 3 Towards the Continuum SYK model8 3.1 Non-commutative SYK8 4 From Minimal Strings to SYK 10 4.1 SYK and the (p; q) spectral curve 11 4.2 FZZT brane correlation function 12 4.3 Minimal String-SYK phase diagram 13 5 SYK as a Non-Critical String 14 6 Conclusion 16 A D-branes in Minimal String Theory 18 A.1 Matrices and the non-commutative torus 23 A.2 Non-commutative SYK 24 A.3 Matrix SYK 26 A.4 Mapping between Matrix SYK and Non-Commutative SYK 27 { 1 { 1 Introduction The SYK model is the prototype of a maximally chaotic quantum system with low energy dynamics given by near-AdS2 gravity. -
Eternal Inflation and Its Implications
IOP PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND THEORETICAL J. Phys. A: Math. Theor. 40 (2007) 6811–6826 doi:10.1088/1751-8113/40/25/S25 Eternal inflation and its implications Alan H Guth Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA E-mail: [email protected] Received 8 February 2006 Published 6 June 2007 Online at stacks.iop.org/JPhysA/40/6811 Abstract Isummarizetheargumentsthatstronglysuggestthatouruniverseisthe product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region. PACS numbers: 98.80.cQ, 98.80.Bp, 98.80.Es 1. Introduction: the successes of inflation Since the proposal of the inflationary model some 25 years ago [1–4], inflation has been remarkably successful in explaining many important qualitative and quantitative properties of the universe. In this paper, I will summarize the key successes, and then discuss a number of issues associated with the eternal nature of inflation. -
Pitp Lectures
MIFPA-10-34 PiTP Lectures Katrin Becker1 Department of Physics, Texas A&M University, College Station, TX 77843, USA [email protected] Contents 1 Introduction 2 2 String duality 3 2.1 T-duality and closed bosonic strings .................... 3 2.2 T-duality and open strings ......................... 4 2.3 Buscher rules ................................ 5 3 Low-energy effective actions 5 3.1 Type II theories ............................... 5 3.1.1 Massless bosons ........................... 6 3.1.2 Charges of D-branes ........................ 7 3.1.3 T-duality for type II theories .................... 7 3.1.4 Low-energy effective actions .................... 8 3.2 M-theory ................................... 8 3.2.1 2-derivative action ......................... 8 3.2.2 8-derivative action ......................... 9 3.3 Type IIB and F-theory ........................... 9 3.4 Type I .................................... 13 3.5 SO(32) heterotic string ........................... 13 4 Compactification and moduli 14 4.1 The torus .................................. 14 4.2 Calabi-Yau 3-folds ............................. 16 5 M-theory compactified on Calabi-Yau 4-folds 17 5.1 The supersymmetric flux background ................... 18 5.2 The warp factor ............................... 18 5.3 SUSY breaking solutions .......................... 19 1 These are two lectures dealing with supersymmetry (SUSY) for branes and strings. These lectures are mainly based on ref. [1] which the reader should consult for original references and additional discussions. 1 Introduction To make contact between superstring theory and the real world we have to understand the vacua of the theory. Of particular interest for vacuum construction are, on the one hand, D-branes. These are hyper-planes on which open strings can end. On the world-volume of coincident D-branes, non-abelian gauge fields can exist. -
Duality and the Nature of Quantum Space-Time
Duality and the nature of quantum space-time Sanjaye Ramgoolam Queen Mary, University of London Oxford, January 24, 2009 INTRODUCTION Strings provide a working theory of quantum gravity existing in harmony with particle physics Successes include computations of quantum graviton scattering, new models of beyond-standard-model particle physics based on branes, computation of black hole entropy A powerful new discovery : Duality I An unexpected equivalence between two systems, which a priori look completely unrelated, if not manifest opposites. I Large and Small (T-duality) I Gravitational and non-Gravitational. (Gauge-String duality) Unification and Duality I They are both powerful results of string theory. They allow us to calculate things we could not calculate before. I Unification : We asked for it and found it. We kind of know why it had to be there. I Duality : We didn’t ask for it. We use it. We don’t know what it really means. Unification v/s Duality I Unification has an illustrious history dating back to the days of Maxwell. I Before Maxwell, we thought magnets attracting iron on the one hand and lightning on the other had nothing to do with each other I After Maxwell : Magnets produce B-field. Electric discharge in lightning is caused by E-fields. The coupled equations of both allow fluctuating E, B-fields which transport energy travelling at the speed of light. In fact light is electromagnetic waves. Unification v/s Duality I Einstein tried to unify gravity with quantum phsyics. I String Theory goes a long way. I Computes graviton interaction probablities. -
Extraordinary Year for Gates Graduate Awards P.3 Staff Awards & Luncheon P.4 in January, President Obama Named Sylvester James Gates, Jr
the ONLINE PHOTONNEWSLETTER FROM UMD DEPARTMENT OF PHYSICS 2012‐2013 Ryan K Morris/Naonal Science & Technology Medals Foundaon this issue AAAS Fellows P.2 Extraordinary Year for Gates Graduate Awards P.3 Staff Awards & Luncheon P.4 In January, President Obama named Sylvester James Gates, Jr. as one of this New Faces P.5 year's recipients of the Naonal Medal of Science. The Naonal Medal of Science and the Naonal Medal of Technology and Innovaon are the highest honors be‐ stowed by the United States Government upon sciensts, engineers and inven‐ Gates on C‐SPAN’s Q & A tors. The honor was one of four in an extraordinary year for Gates. Most recently, Gates was awarded the 2013 Mendel Medal by Villanova Universi‐ Jim Gates discusses science educaon, string theory, working ty. The honor recognizes pioneering sciensts who have demonstrated, by their with the President almost becom‐ lives and their standing before the world as sciensts, that there is no intrinsic ing an astronaut and being mistak‐ conflict between science and religion. Addionally, Gates was one of 84 U.S. re‐ en for Morgan Freeman on C‐ searchers and 21 foreign associates elected to the Naonal Academy of Science. SPAN’s Q & A The interview Elecon to the academy is considered one of the highest honors that can be ac‐ transcript is available on the Q & A website or watch the video at corded a U.S. scienst or engineer. And in January he was named a University Sys‐ tem of Maryland (USM) Regents Professor, the System's most prominent faculty hp://www.c‐spanvideo.org/ recognion. -
N = 1 Field Theory Duality from M-Theory
hep-th/9708015 BUHEP-97-23 N = 1 Field Theory Duality from M-theory Martin Schmaltz and Raman Sundrum Department of Physics Boston University Boston, MA 02215, USA [email protected], [email protected] Abstract We investigate Seiberg’s N = 1 field theory duality for four-dimensional super- symmetric QCD with the M-theory 5-brane. We find that the M-theory configuration for the magnetic dual theory arises via a smooth deformation of the M-theory config- arXiv:hep-th/9708015v2 27 Aug 1997 uration for the electric theory. The creation of Dirichlet 4-branes as Neveu-Schwarz 5-branes are passed through each other in Type IIA string theory is given a nice derivation from M-theory. 1 Introduction In the last few years there has been tremendous progress in understanding supersym- metric gauge dynamics and the remarkable phenomenon of electric-magnetic duality [1, 2]. Most of the results were first guessed at within field theory and then checked to satisfy many non-trivial consistency conditions. However, the organizing principle behind these dualities has always been somewhat mysterious from the field theoretic perspective. Recently there has arisen a fascinating connection between supersymmetric gauge dynamics and string theory brane dynamics [3] which has the potential for unifying our understanding of these dualities [4-13]. This stems from our ability to set up configurations of branes in string theory with supersymmetric gauge field theories living on the world-volumes of branes in the low-energy limit. The moduli spaces of the gauge field theories are thereby encoded geometrically in the brane set-up. -
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. -
LOCALIZATION and STRING DUALITY 1. Introduction According
LOCALIZATION AND STRING DUALITY KEFENG LIU 1. Introduction According to string theorists, String Theory, as the most promising candidate for the grand unification of all fundamental forces in the nature, should be the final theory of the world, and should be unique. But now there are five different looking string theories. As argued by the physicists, these theories should be equivalent, in a way dual to each other. On the other hand all previous theories like the Yang-Mills and the Chern-Simons theory should be parts of string theory. In particular their partition functions should be equal or equivalent to each other in the sense that they are equal after certain transformation. To compute partition functions, physicists use localization technique, a modern version of residue theorem, on infinite dimen- sional spaces. More precisely they apply localization formally to path integrals which is not well-defined yet in mathematics. In many cases such computations reduce the path integrals to certain integrals of various Chern classes on various finite dimensional moduli spaces, such as the moduli spaces of stable maps and the moduli spaces of vector bundles. The identifications of these partition functions among different theories have produced many surprisingly beautiful mathematical formulas like the famous mirror formula [22], as well as the Mari˜no-Vafa formula [25]. The mathematical proofs of these formulas from the string duality also depend on localization techniques on these various finite dimensional moduli spaces. The purpose of this note is to discuss our recent work on the subject. I will briefly discuss the proof of the Marin˜o-Vafa formula, its generalizations and the related topological vertex theory [1].