DOCSLIB.ORG

Almost 50 Years with String Theory

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Almost 50 Years with String Theory Almost 50 Years with String Theory: A framework to formulate from the Planck length to the Hubble radius M.M. Sheikh-Jabbari Iranian Physics Society, Annual meeting on particle physics and fields Isfahan, Bahman 1394 1 • In 1968, string theory was born through a paper by G. Veneziano On Dual Resonance Model, as an effective theory for hadrons. • Since then, in almost 50 years, string theory has undergone many ups and downs, commonly known as string theory revolutions. • Despite these “revolutions,” a satisfactory understanding of string theory is still missing. • This talk is devoted to presenting the current status of string theory from a historical viewpoint. 2 On the timeline of string theory, and its revolutions • Late 1960’s, birth of string theory and “dual resonance models.” • 1974-5, first revolution: String theory contains massless spin two particles, string theory as a theory of gravity. • 1984-5, second revolution, cancellation of anomalies in superstring theories, string theory as a theory of quantum gravity. • 1994-95, third revolution, dualities, birth of M-theory, D-branes. • 1997-98, fourth revolution, AdS/CFT presented and formulated. • 2000’s, fifth revolution/revelation: String Theory landscape. • Current status and future expected revolutions/breakthroughs. 3 On the birth of string theory: • By early 1960’s hadron physics was in full bloom, there was a zoo of hadronic particles, resonances, found in (deep) inelastic scattering experiments. • Gell-Mann’s quark model, was nicely accommodating these parti- cles, mesons and baryons. Nonetheless, it did not contain dynam- ics, the cross-sections and decay rates. • “Strong interactions” was thought not to be described by a quan- tum field theory. • This led people to think outside the field theory models of the time. The S-matrix theory developed in this atmosphere. 4 • The “sum rules” and phenomenological formulas describing “res- onance”, their mass and width, was very common. • In 1968, Veneziano wrote a “dual resonance model,” which was compatible with the mass to spin ratio predicted by Regge. • Veneziano’s model predicted infinitely many hadrons and their scat- tering amplitude as a function of their mass and spin. • In 1969-70, Nambu, Nielsen, and Susskind realized independently, through a study of poles of the Veneziano amplitude (as pointed out by Hagedorn in 60’s), that these poles coincides with energy levels in vibrating modes of a string. • However, the course of dual models was in decline.... 5 • In 1972-73, ’t Hooft and Veltman showed renormalizability of Yang- Mills theories and, soon after Gross, Wilczek and Politzer estab- lished asymptotic freedom. • In 1973-74, the quantum field theory model for strong interaction, Quantum Chromo Dynamics, was proposed. • During 1973-76, some people tried to dismiss QCD or the “dual resonance model” in favor of the other and some tried to reconcile them. • The experimental evidence (deep inelastic scattering) was piling up in favor of the quark model and the QCD, and implicitly against the dual model. 6 First revolution: String theory is a theory of gravity. • In 1974, J. Schwarz and J. Scherk, and independently T. Yoneya, noted that the spectrum of “dual resonance model” contained massless spin two particles. • But, this theory had its own issues, it had tachyons in its spectrum. • In 1976, S. Deser, B. Zumino, and independently L. Brink, P. Di Vecchia, P. Howe, wrote the string worldsheet action. • In 1981, A. Polyakov quantized the worldsheet action. 7 • In the rest of 1970’ and early 1980’s, it was noted that – there are open strings as well as closed strings. The latter have massless spin two, while the former a massless vector boson. – the theory of bosonic strings is well-defined in 26 dimensions. – Interaction of strings (via joining and splitting of the endpoints) was formulated in the light-cone gauge. – Strings had tachyon in their spectrum. – “Bosonic String” theory has no fermions in its spectrum. – Most of string computations were done in light-cone gauge and it was not clear whether these results are gauge-independent and whether light-cone gauge captures the whole theory. 8 Other relevant technical developments of the era: • Supersymmetry was proposed in 1971-72 (several people are at- tributed to it). • In 1974 Wess and Zumino showed the first example of non-renormalization properties of supersymmetric field theories. • Supersymmetry proved a very useful technical tool in taming loop effects and runnings. The era of SUSY-gauge theories had began. • In the 1975 and 1976 theories with local supersymmetry, super- gravity, were introduced by Arnowitt, Nath and Ferrara, Freedman, Van Nieuwenhuizen. 9 Other relevant technical developments of the era, cont’d: • SUGRA was continued in many different ways (Abdus Salam was one of its main advocates) and is still an active field of research. • From the early days in 1971, supersymmetry and string theory (of Schwarz, Ramond and Neveu) had intimate relations. • K. Settle in 1976 (see also his 1978 paper) wrote a very influential paper on renormalizability of higher derivative gravity theories. • Blavin-Polyakov-Zamolodchikov in 1984 developed the 2d confor- mal field theory which was extensively used for further development of string worldsheet theory. • Alvarez-Gaume and Witten in 1983 analyzed chiral anomaly in su- pergraivty theories. 10 Second revolution: String theory is a theory of quantum gravity. • Superstring theory was formulated in early 1980’s. Two ways to add SUSY: – Via supersymmetry on the worldsheet (Ramond-Neveu-Schwarz) + Gliozzi-Scherk-Olive (GSO) projection, or – through imposing superymmetry both on the worldsheet and on target space (Green-Schwarz formulation). • Superstring theory is consistently formulated in 10dim (critical string theories). • By 1984 three 10dim. superstring theories were known: type IIA, type IIB and type I. The first two were closed string theories and type I includes both open and closed strings. 12 • In 1984 M. Green and J. Schwarz proved that type IIB and type I theories are anomaly free. • In 1985 two more superstring theories found (Gross-Harvey-Martinec and Rohm): Het SO(32) and Het E8 × E8: • There are FIVE 10d superstring theories which are anomaly free. • We only knew how to formulate them perturbatively using world- sheet 2d CFT techniques. • It was shown that superstring theory is one-loop renormalizable. 13 String compactifications, infinitly many string theories. • Although it was portrayed as a unifying theory, because in 10d. it has only one parameter gs a scale ℓs it. • But usual physics is in 4d. Four dimensional theories can be ob- tained via Kaluza-Klein reduction or compactification. 4 • For R × M6 background, there are infinitely many choices for M6. • Geometric properties of M6 appear as physical parameters of 4d theory. So, there are potentially infinitely many 4d string theories. • Specific requirements about 4d theory can restrict M6, but as it has become very clear now, in no ways fixes it. 14 Third revolution: Dualities as the unifying theme; Discovery of D-branes. • This unfortunate feature motivated string theorist to accept in- finitely many theories as a feature and cure the problem in an ingenuous way: All these theories are equivalent, they are dual to each other. • Idea of dualities was known in the context of QFT’s and string theory: – S-duality, like Electric-Magentic duality. 2 – T-duality, string theories on circles with radius R and ℓs /R are equal. • A good part of 1990’s was devoted to developing web of dualities. 15 • Dualities opened the way to discuss beyond perturbative, weakly coupled theories. • Exploring dualities was very fruitful: – Dualities were essential to considerably reduce the number of independent lower dimensional string theories. – A more fundamental M-theory was proposed. Low energy ef- fective theory of M-theory is the 11d SUGRA. – T plus S duality led to discovery of D-branes (Polchinski, 1995). – The important property of D-branes is that there is a U(N) gauge theory structure associated with N coincident D-branes. (Witten, 1995). 16 D-branes on their own turn were the key to all post-1995 developments in string theory: • D-branes were used to propose the M(atrix) model formulation for M-theory (Banks-Fishler-Shenker-Susskind, 1996). • D-branes were used to model certain BPS black holes within string theory and propose black hole microstate counting. (Strominger and Vafa, 1996.) • Brane configurations were essential for modelling supersymmetric gauge theories within string theory setup and giving a simple, geo- metric picture for non-perturbative analysis of SUSY gauge theories (Mainly due to Witten, 1996-97.) • Most importantly, D-branes led to AdS/CFT (Maldacena, 1997). 17 Fourth revolution: The AdS/CFT • D-branes may be described by their low energy effective theory, a U(N) SUSY gauge theory, or by viewing them as sources for energy momentum tensor, solutions to SUGRA. • This dual description led J. Maldacena to the AdS/CFT proposal: Maximally SUSY d- dimensional gauge theories at their conformal × D−d−1 fixed line (point) is dual to string theory on AdSd+1 S back- ground. • This duality was given a very precise meaning and formulation by Gubser-Klebanov-Polyakov and independently by Witten in early 1998. 18 • This duality has been extended to gauge theories with almost ar- bitrary gauge group and matter content. • This duality has been a key player of the developments of string theory and HEP-TH in general. • A more relaxed, less robust, but very useful statement of AdS/CFT is gauge/gravity correspondence: Einstein gravity on a weakly curved background describes strongly coupled gauge theories at large N. • Gauge/gravity correspondence has been used as a very powerful tool to address regimes in QFT where usual perturbative tools fail. 19 The AdS/CFT duality or gauge/gravity correspondence • have changed our understanding of QFT (beyond the Wilsonian formulation).
Load more

Recommended publications
  • Particles-Versus-Strings.Pdf
    Particles vs. strings http://insti.physics.sunysb.edu/~siegel/vs.html In light of the huge amount of propaganda and confusion regarding string theory, it might be useful to consider the relative merits of the descriptions of the fundamental constituents of matter as particles or strings. (More-skeptical reviews can be found in my physics parodies.A more technical analysis can be found at "Warren Siegel's research".) Predictability The main problem in high energy theoretical physics today is predictions, especially for quantum gravity and confinement. An important part of predictability is calculability. There are various levels of calculations possible: 1. Existence: proofs of theorems, answers to yes/no questions 2. Qualitative: "hand-waving" results, answers to multiple choice questions 3. Order of magnitude: dimensional analysis arguments, 10? (but beware hidden numbers, like powers of 4π) 4. Constants: generally low-energy results, like ground-state energies 5. Functions: complete results, like scattering probabilities in terms of energy and angle Any but the last level eventually leads to rejection of the theory, although previous levels are acceptable at early stages, as long as progress is encouraging. It is easy to write down the most general theory consistent with special (and for gravity, general) relativity, quantum mechanics, and field theory, but it is too general: The spectrum of particles must be specified, and more coupling constants and varieties of interaction become available as energy increases. The solutions to this problem go by various names -- "unification", "renormalizability", "finiteness", "universality", etc. -- but they are all just different ways to realize the same goal of predictability.
    [Show full text]
  • Hep-Th/0011078V1 9 Nov 2000 1 Okspotdi Atb H ..Dp.O Nryudrgrant Under Energy of Dept
    CALT-68-2300 CITUSC/00-060 hep-th/0011078 String Theory Origins of Supersymmetry1 John H. Schwarz California Institute of Technology, Pasadena, CA 91125, USA and Caltech-USC Center for Theoretical Physics University of Southern California, Los Angeles, CA 90089, USA Abstract The string theory introduced in early 1971 by Ramond, Neveu, and myself has two-dimensional world-sheet supersymmetry. This theory, developed at about the same time that Golfand and Likhtman constructed the four-dimensional super-Poincar´ealgebra, motivated Wess and Zumino to construct supersymmet- ric field theories in four dimensions. Gliozzi, Scherk, and Olive conjectured the arXiv:hep-th/0011078v1 9 Nov 2000 spacetime supersymmetry of the string theory in 1976, a fact that was proved five years later by Green and myself. Presented at the Conference 30 Years of Supersymmetry 1Work supported in part by the U.S. Dept. of Energy under Grant No. DE-FG03-92-ER40701. 1 S-Matrix Theory, Duality, and the Bootstrap In the late 1960s there were two parallel trends in particle physics. On the one hand, many hadron resonances were discovered, making it quite clear that hadrons are not elementary particles. In fact, they were found, to good approximation, to lie on linear parallel Regge trajectories, which supported the notion that they are composite. Moreover, high energy scattering data displayed Regge asymptotic behavior that could be explained by the extrap- olation of the same Regge trajectories, as well as one with vacuum quantum numbers called the Pomeron. This set of developments was the focus of the S-Matrix Theory community of theorists.
    [Show full text]
  • Strings, Boundary Fermions and Coincident D-Branes
    Strings, boundary fermions and coincident D-branes Linus Wulff Department of Physics Stockholm University Thesis for the degree of Doctor of Philosophy in Theoretical Physics Department of Physics, Stockholm University Sweden c Linus Wulff, Stockholm 2007 ISBN 91-7155-371-1 pp 1-85 Printed in Sweden by Universitetsservice US-AB, Stockholm 2007 Abstract The appearance in string theory of higher-dimensional objects known as D- branes has been a source of much of the interesting developements in the subject during the past ten years. A very interesting phenomenon occurs when several of these D-branes are made to coincide: The abelian gauge theory liv- ing on each brane is enhanced to a non-abelian gauge theory living on the stack of coincident branes. This gives rise to interesting effects like the natural ap- pearance of non-commutative geometry. The theory governing the dynamics of these coincident branes is still poorly understood however and only hints of the underlying structure have been seen. This thesis focuses on an attempt to better this understanding by writing down actions for coincident branes using so-called boundary fermions, orig- inating in considerations of open strings, instead of matrices to describe the non-abelian fields. It is shown that by gauge-fixing and by suitably quantiz- ing these boundary fermions the non-abelian action that is known, the Myers action, can be reproduced. Furthermore it is shown that under natural assump- tions, unlike the Myers action, the action formulated using boundary fermions also posseses kappa-symmetry, the criterion for being the correct supersym- metric action for coincident D-branes.
    [Show full text]
  • Notas De Física CBPF-NF-007/10 February 2010
    ISSN 0029-3865 CBPF - CENTRO BRASILEIRO DE PESQUISAS FíSICAS Rio de Janeiro Notas de Física CBPF-NF-007/10 February 2010 A criticaI Iook at 50 years particle theory from the perspective of the crossing property Bert Schroer Ministét"iQ da Ciência e Tecnologia A critical look at 50 years particle theory from the perspective of the crossing property Dedicated to Ivan Todorov on the occasion of his 75th birthday to be published in Foundations of Physics Bert Schroer CBPF, Rua Dr. Xavier Sigaud 150 22290-180 Rio de Janeiro, Brazil and Institut fuer Theoretische Physik der FU Berlin, Germany December 2009 Contents 1 The increasing gap between foundational work and particle theory 2 2 The crossing property and the S-matrix bootstrap approach 7 3 The dual resonance model, superseded phenomenology or progenitor of a new fundamental theory? 15 4 String theory, a TOE or a tower of Babel within particle theory? 21 5 Relation between modular localization and the crossing property 28 6 An exceptional case of localization equivalence: d=1+1 factorizing mod- els 35 7 Resum´e, some personal observations and a somewhat downbeat outlook 39 8 Appendix: a sketch of modular localization 47 8.1 Modular localization of states . 47 8.2 Localized subalgebras . 51 CBPF-NF-007/10 CBPF-NF-007/10 2 Abstract The crossing property, which originated more than 5 decades ago in the after- math of dispersion relations, was the central new concept which opened an S-matrix based line of research in particle theory. Many constructive ideas in particle theory outside perturbative QFT, among them the S-matrix bootstrap program, the dual resonance model and the various stages of string theory have their historical roots in this property.
    [Show full text]
  • 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
    [Show full text]
  • 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.
    [Show full text]
  • Notes on String Theory
    Notes on String Theory Universidad de Santiago de Compostela April 2, 2013 Contents 1 Strings from gauge theories 3 1.1 Introduction . .3 1.2 The dual resonance model . .3 1.3 Regge trajectories from String Theory . .7 1.4 String theory from the large Nc counting of gauge theories . .8 2 Open and Closed String Amplitudes 13 2.1 Closed string interactions . 13 2.2 S matrix and Scattering Amplitudes . 18 2.2.1 m-point amplitudes for closed strings. 18 2.2.2 4-point tachyon amplitude . 21 2.3 Open string scattering . 24 3 Gauge theory from string theory 29 3.1 Gauge theory from open strings . 29 3.2 Gauge theory from closed strings . 30 3.2.1 The Kaluza Klein reduction . 30 3.2.2 Closed strings on a circle . 31 3.2.3 Massless spectrum . 33 3.3 T- duality . 33 3.3.1 Full spectrum: T-duality for closed strings . 34 3.3.2 Enhanced gauge symmetry: . 34 4 D-branes 35 4.1 T-duality for open strings and D-branes . 35 4.1.1 D branes . 36 4.1.2 T-duality with Wilson Lines . 36 4.1.3 T-duality for type II superstrings . 37 4.2 Dynamics of D − branes ............................. 39 1 4.2.1 Born-Infeld action . 40 2 Chapter 1 Strings from gauge theories 1.1 Introduction We can safely trace the origins of strings to the early 50's, where lots of scattering experi- ments were performed involving mesons and baryons. The evidence of a parton substruc- ture, together with the impossibility to obtain the quarks as a individual final states lead to the conclusion that confinement is a built in property of non abelian gauge theories.
    [Show full text]
  • The Scientific Contributions of Jo¨El Scherk
    CALT-68-2723 THE SCIENTIFIC CONTRIBUTIONS OF JOEL¨ SCHERK John H. Schwarz California Institute of Technology Pasadena, CA 91125, USA Abstract Jo¨el Scherk (1946–1980) was an important early contributor to the development of string theory. Together with various collaborators, he made numerous pro- found and influential contributions to the subject throughout the decade of the 1970s. On the occasion of a conference at the Ecole´ Normale Sup´erieure in 2000 that was dedicated to the memory of Jo¨el Scherk I gave a talk entitled “Reminis- cences of Collaborations with Jo¨el Scherk” [1]. The present article, an expanded arXiv:0904.0537v1 [hep-th] 3 Apr 2009 version of that one, also discusses work in which I was not involved. Contribution to a volume entitled The Birth of String Theory 1 Introduction Jo¨el Scherk and Andr´eNeveu were two brilliant French theoretical physicists who emerged in the latter part of the 1960s. They were students together at the elite Ecole´ Normale Sup´erieure in Paris and in Orsay, where they studied electromagnetic and final-state interac- tion corrections to nonleptonic kaon decays [2] under the guidance of Claude Bouchiat and Philippe Meyer. They defended their “th`ese de troisi`eme cycle” (the French equivalent of a PhD) in 1969, and they were hired together by the CNRS that year [3]. (Tenure at age 23!) In September 1969 the two of them headed off to Princeton University. Jo¨el was supported by a NATO Fellowship.1 In 1969 my duties as an Assistant Professor in Princeton included advising some assigned graduate students.
    [Show full text]
  • The Birth of String Theory
    The Birth of String Theory Edited by Andrea Cappelli INFN, Florence Elena Castellani Department of Philosophy, University of Florence Filippo Colomo INFN, Florence Paolo Di Vecchia The Niels Bohr Institute, Copenhagen and Nordita, Stockholm Contents Contributors page vii Preface xi Contents of Editors' Chapters xiv Abbreviations and acronyms xviii Photographs of contributors xxi Part I Overview 1 1 Introduction and synopsis 3 2 Rise and fall of the hadronic string Gabriele Veneziano 19 3 Gravity, unification, and the superstring John H. Schwarz 41 4 Early string theory as a challenging case study for philo- sophers Elena Castellani 71 EARLY STRING THEORY 91 Part II The prehistory: the analytic S-matrix 93 5 Introduction to Part II 95 6 Particle theory in the Sixties: from current algebra to the Veneziano amplitude Marco Ademollo 115 7 The path to the Veneziano model Hector R. Rubinstein 134 iii iv Contents 8 Two-component duality and strings Peter G.O. Freund 141 9 Note on the prehistory of string theory Murray Gell-Mann 148 Part III The Dual Resonance Model 151 10 Introduction to Part III 153 11 From the S-matrix to string theory Paolo Di Vecchia 178 12 Reminiscence on the birth of string theory Joel A. Shapiro 204 13 Personal recollections Daniele Amati 219 14 Early string theory at Fermilab and Rutgers Louis Clavelli 221 15 Dual amplitudes in higher dimensions: a personal view Claud Lovelace 227 16 Personal recollections on dual models Renato Musto 232 17 Remembering the `supergroup' collaboration Francesco Nicodemi 239 18 The `3-Reggeon vertex' Stefano Sciuto 246 Part IV The string 251 19 Introduction to Part IV 253 20 From dual models to relativistic strings Peter Goddard 270 21 The first string theory: personal recollections Leonard Susskind 301 22 The string picture of the Veneziano model Holger B.
    [Show full text]
  • Yukawa Couplings from D-Branes on Non-Factorisable Tori
    Yukawa Couplings from D-branes on non-factorisable Tori Dissertation zur Erlangung des Doktorgrades (Dr. rer. nat.) der Mathematisch-Naturwissenschaftlichen Fakultät der Rheinischen Friedrich-Wilhelms-Universität Bonn von Chatura Christoph Liyanage aus Bonn Bonn, 2018 Dieser Forschungsbericht wurde als Dissertation von der Mathematisch-Naturwissenschaftlichen Fakultät der Universität Bonn angenommen und ist auf dem Hochschulschriftenserver der ULB Bonn http://hss.ulb.uni-bonn.de/diss_online elektronisch publiziert. 1. Gutachter: Priv. Doz. Dr. Stefan Förste 2. Gutachter: Prof. Dr. Albrecht Klemm Tag der Promotion: 05.07.2018 Erscheinungsjahr: 2018 CHAPTER 1 Abstract In this thesis Yukawa couplings from D-branes on non-factorisable tori are computed. In particular intersecting D6-branes on the torus, generated by the SO(12) root lattice, is considered, where the Yukawa couplings arise from worldsheet instantons. Thereby the classical part to the Yukawa couplings are determined and known expressions for Yukawa couplings on factorisable tori are extended. Further Yukawa couplings for the T-dual setup are computed. Therefor three directions of the SO(12) torus are T-dualized and the boundary conditions of the D6-branes are translated to magnetic fluxes on the torus. Wavefunctions for chiral matter are calculated, where the expressions, known from the factorisable case, get modified in a non-trivial way. Integration of three wavefunctions over the non-factorisable torus yields the Yukawa couplings. The result not only confirms the results from the computations on the SO(12) torus, but also determines the quantum contribution to the couplings. This thesis also contains a brief review to intersecting D6-branes on Z2 ×Z2 orientifolds, with applications to a non-factorisable orientifold, generated by the SO(12) root lattice.
    [Show full text]
  • Brown University Theoretical and Experimental Studies of High
    Senior Thesis Brown University Department of Physics Theoretical and Experimental Studies of High-Energy Processes in QCD CMS Preliminary 19.7 fb-1 (8 TeV) 10000 9000 Data tt Events Drell Yann 8000 Single Top W+Jets Multi-bosons 7000 Uncertainty 6000 5000 kc 4000 ka¯ k¯b z3 3000 z z 1 2 2000 α (t1) α (t2) 1000 ka kb kc¯ 0 1.2 1 0.8 100 150 200 250 300 350 400 450 AMWT mass [GeV] Author: Advisors: Richard Nally Prof. Chung-I Tan Prof. Meenakshi Narain April 2015 Contents Overview 3 p I Measurement of the Top Quark Mass in Fully Leptonic Decays at s = 8 TeV with the Full 2012 CMS Dataset 4 I.1 Introduction 5 I.2 Datasets and MC Samples 5 I.3 Event Selection 7 I.3.1 Event Cleaning . 7 I.3.2 Trigger Selection . 8 I.3.3 Lepton Reconstruction and Selection . 8 I.3.3.1 Muon Reconstruction and Selection . 8 I.3.3.2 Electron Reconstruction and Selection . 9 I.3.4 Jet Selection and Missing Transverse Momentum . 9 I.3.5 Jet Selection Using b-tagging . 10 I.4 Estimate of the Background Contamination 10 I.5 Event Yields and Data-MC Comparisons 10 I.6 Event Reconstruction 20 I.7 Top Mass Estimate from Template Fits 22 I.7.1 Study of the Method on Simulated Data . 23 I.7.2 Result with Data . 24 I.8 Systematic Uncertainties 27 I.9 Conclusion 29 I.A Transverse momentum based reweighting of the tt¯ Monte Carlo 31 II Computing Inclusive QCD Cross-Sections Through AdS/CFT 34 II.1 Introduction 35 II.2 String Scattering in Flat Space 37 II.2.1 An Overview of Bosonic String Theory .
    [Show full text]
  • String Theory
    SPECIAL SECTION: SUPERSTRINGS – A QUEST FOR A UNIFIED THEORY String theory John H. Schwarz California Institute of Technology, Pasadena, CA 91125, USA energies, it is present in exactly the form proposed by This article presents the basic concepts of string the- Einstein. This is significant, because it is arising within ory followed by an overview of the peculiar history of how it arose. the framework of a consistent quantum theory. Ordinary quantum field theory does not allow gravity to exist; string theory requires it! The second general fact is that MANY of the major developments in fundamental phys- Yang–Mills gauge theories of the sort that comprise the ics of the past century arose from identifying and over- standard model, naturally arise in string theory. We do coming contradictions between existing ideas. For not understand why the specific SU(3) ´ SU(2) ´ U(1) example, the incompatibility of Maxwell’s equations gauge theory of the standard model should be preferred, and Galilean invariance led Einstein to propose the spe- but (anomaly-free) theories of this general type do arise cial theory of relativity. Similarly, the inconsistency of naturally at ordinary energies. The third general feature special relativity with Newtonian gravity led him to of string theory solutions is supersymmetry. The develop the general theory of relativity. More recently, mathematical consistency of string theory depends cru- the reconciliation of special relativity with quantum cially on supersymmetry, and it is very hard to find mechanics led to the development of quantum field the- consistent solutions (quantum vacua) that do not pre- ory.
    [Show full text]