String Theory • This Two Volume Work Is the Standard Introduction to the Subject
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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. -
Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings. -
Duality and Strings Dieter Lüst, LMU and MPI München
Duality and Strings Dieter Lüst, LMU and MPI München Freitag, 15. März 13 Luis made several very profound and important contributions to theoretical physics ! Freitag, 15. März 13 Luis made several very profound and important contributions to theoretical physics ! Often we were working on related subjects and I enjoyed various very nice collaborations and friendship with Luis. Freitag, 15. März 13 Luis made several very profound and important contributions to theoretical physics ! Often we were working on related subjects and I enjoyed various very nice collaborations and friendship with Luis. Duality of 4 - dimensional string constructions: • Covariant lattices ⇔ (a)symmetric orbifolds (1986/87: W. Lerche, D.L., A. Schellekens ⇔ L. Ibanez, H.P. Nilles, F. Quevedo) • Intersecting D-brane models ☞ SM (?) (2000/01: R. Blumenhagen, B. Körs, L. Görlich, D.L., T. Ott ⇔ G. Aldazabal, S. Franco, L. Ibanez, F. Marchesano, R. Rabadan, A. Uranga) Freitag, 15. März 13 Luis made several very profound and important contributions to theoretical physics ! Often we were working on related subjects and I enjoyed various very nice collaborations and friendship with Luis. Duality of 4 - dimensional string constructions: • Covariant lattices ⇔ (a)symmetric orbifolds (1986/87: W. Lerche, D.L., A. Schellekens ⇔ L. Ibanez, H.P. Nilles, F. Quevedo) • Intersecting D-brane models ☞ SM (?) (2000/01: R. Blumenhagen, B. Körs, L. Görlich, D.L., T. Ott ⇔ G. Aldazabal, S. Franco, L. Ibanez, F. Marchesano, R. Rabadan, A. Uranga) ➢ Madrid (Spanish) Quiver ! Freitag, 15. März 13 Luis made several very profound and important contributions to theoretical physics ! Often we were working on related subjects and I enjoyed various very nice collaborations and friendship with Luis. -
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. -
From Vibrating Strings to a Unified Theory of All Interactions
Barton Zwiebach From Vibrating Strings to a Unified Theory of All Interactions or the last twenty years, physicists have investigated F String Theory rather vigorously. The theory has revealed an unusual depth. As a result, despite much progress in our under- standing of its remarkable properties, basic features of the theory remain a mystery. This extended period of activity is, in fact, the second period of activity in string theory. When it was first discov- ered in the late 1960s, string theory attempted to describe strongly interacting particles. Along came Quantum Chromodynamics— a theoryof quarks and gluons—and despite their early promise, strings faded away. This time string theory is a credible candidate for a theoryof all interactions—a unified theoryof all forces and matter. The greatest complication that frustrated the search for such a unified theorywas the incompatibility between two pillars of twen- tieth century physics: Einstein’s General Theoryof Relativity and the principles of Quantum Mechanics. String theory appears to be 30 ) zwiebach mit physics annual 2004 the long-sought quantum mechani- cal theory of gravity and other interactions. It is almost certain that string theory is a consistent theory. It is less certain that it describes our real world. Nevertheless, intense work has demonstrated that string theory incorporates many features of the physical universe. It is reasonable to be very optimistic about the prospects of string theory. Perhaps one of the most impressive features of string theory is the appearance of gravity as one of the fluctuation modes of a closed string. Although it was not discov- ered exactly in this way, we can describe a logical path that leads to the discovery of gravity in string theory. -
Introduction to Conformal Field Theory and String
SLAC-PUB-5149 December 1989 m INTRODUCTION TO CONFORMAL FIELD THEORY AND STRING THEORY* Lance J. Dixon Stanford Linear Accelerator Center Stanford University Stanford, CA 94309 ABSTRACT I give an elementary introduction to conformal field theory and its applications to string theory. I. INTRODUCTION: These lectures are meant to provide a brief introduction to conformal field -theory (CFT) and string theory for those with no prior exposure to the subjects. There are many excellent reviews already available (or almost available), and most of these go in to much more detail than I will be able to here. Those reviews con- centrating on the CFT side of the subject include refs. 1,2,3,4; those emphasizing string theory include refs. 5,6,7,8,9,10,11,12,13 I will start with a little pre-history of string theory to help motivate the sub- ject. In the 1960’s it was noticed that certain properties of the hadronic spectrum - squared masses for resonances that rose linearly with the angular momentum - resembled the excitations of a massless, relativistic string.14 Such a string is char- *Work supported in by the Department of Energy, contract DE-AC03-76SF00515. Lectures presented at the Theoretical Advanced Study Institute In Elementary Particle Physics, Boulder, Colorado, June 4-30,1989 acterized by just one energy (or length) scale,* namely the square root of the string tension T, which is the energy per unit length of a static, stretched string. For strings to describe the strong interactions fi should be of order 1 GeV. Although strings provided a qualitative understanding of much hadronic physics (and are still useful today for describing hadronic spectra 15 and fragmentation16), some features were hard to reconcile. -
Three Duality Symmetries Between Photons and Cosmic String Loops, and Macro and Micro Black Holes
Symmetry 2015, 7, 2134-2149; doi:10.3390/sym7042134 OPEN ACCESS symmetry ISSN 2073-8994 www.mdpi.com/journal/symmetry Article Three Duality Symmetries between Photons and Cosmic String Loops, and Macro and Micro Black Holes David Jou 1;2;*, Michele Sciacca 1;3;4;* and Maria Stella Mongiovì 4;5 1 Departament de Física, Universitat Autònoma de Barcelona, Bellaterra 08193, Spain 2 Institut d’Estudis Catalans, Carme 47, Barcelona 08001, Spain 3 Dipartimento di Scienze Agrarie e Forestali, Università di Palermo, Viale delle Scienze, Palermo 90128, Italy 4 Istituto Nazionale di Alta Matematica, Roma 00185 , Italy 5 Dipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica (DICGIM), Università di Palermo, Viale delle Scienze, Palermo 90128, Italy; E-Mail: [email protected] * Authors to whom correspondence should be addressed; E-Mails: [email protected] (D.J.); [email protected] (M.S.); Tel.: +34-93-581-1658 (D.J.); +39-091-23897084 (M.S.). Academic Editor: Sergei Odintsov Received: 22 September 2015 / Accepted: 9 November 2015 / Published: 17 November 2015 Abstract: We present a review of two thermal duality symmetries between two different kinds of systems: photons and cosmic string loops, and macro black holes and micro black holes, respectively. It also follows a third joint duality symmetry amongst them through thermal equilibrium and stability between macro black holes and photon gas, and micro black holes and string loop gas, respectively. The possible cosmological consequences of these symmetries are discussed. Keywords: photons; cosmic string loops; black holes thermodynamics; duality symmetry 1. Introduction Thermal duality relates high-energy and low-energy states of corresponding dual systems in such a way that the thermal properties of a state of one of them at some temperature T are related to the properties of a state of the other system at temperature 1=T [1–6]. -
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. -
Introduction to String Theory A.N
Introduction to String Theory A.N. Schellekens Based on lectures given at the Radboud Universiteit, Nijmegen Last update 6 July 2016 [Word cloud by www.worldle.net] Contents 1 Current Problems in Particle Physics7 1.1 Problems of Quantum Gravity.........................9 1.2 String Diagrams................................. 11 2 Bosonic String Action 15 2.1 The Relativistic Point Particle......................... 15 2.2 The Nambu-Goto action............................ 16 2.3 The Free Boson Action............................. 16 2.4 World sheet versus Space-time......................... 18 2.5 Symmetries................................... 19 2.6 Conformal Gauge................................ 20 2.7 The Equations of Motion............................ 21 2.8 Conformal Invariance.............................. 22 3 String Spectra 24 3.1 Mode Expansion................................ 24 3.1.1 Closed Strings.............................. 24 3.1.2 Open String Boundary Conditions................... 25 3.1.3 Open String Mode Expansion..................... 26 3.1.4 Open versus Closed........................... 26 3.2 Quantization.................................. 26 3.3 Negative Norm States............................. 27 3.4 Constraints................................... 28 3.5 Mode Expansion of the Constraints...................... 28 3.6 The Virasoro Constraints............................ 29 3.7 Operator Ordering............................... 30 3.8 Commutators of Constraints.......................... 31 3.9 Computation of the Central Charge..................... -
M-Theory Solutions and Intersecting D-Brane Systems
M-Theory Solutions and Intersecting D-Brane Systems A Thesis Submitted to the College of Graduate Studies and Research in Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy in the Department of Physics and Engineering Physics University of Saskatchewan Saskatoon By Rahim Oraji ©Rahim Oraji, December/2011. All rights reserved. Permission to Use In presenting this thesis in partial fulfilment of the requirements for a Postgrad- uate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this thesis in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my thesis work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this thesis or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis. Requests for permission to copy or to make other use of material in this thesis in whole or part should be addressed to: Head of the Department of Physics and Engineering Physics 116 Science Place University of Saskatchewan Saskatoon, Saskatchewan Canada S7N 5E2 i Abstract It is believed that fundamental M-theory in the low-energy limit can be described effectively by D=11 supergravity. -
Achievements, Progress and Open Questions in String Field Theory Strings 2021 ICTP-SAIFR, S˜Ao Paulo June 22, 2021
Achievements, Progress and Open Questions in String Field Theory Strings 2021 ICTP-SAIFR, S˜ao Paulo June 22, 2021 Yuji Okawa and Barton Zwiebach 1 Achievements We consider here instances where string field theory provided the answer to physical open questions. • Tachyon condensation, tachyon vacuum, tachyon conjectures The tachyon conjectures (Sen, 1999) posited that: (a) The tachyon potential has a locally stable minimum, whose energy density measured with respect to that of the unstable critical point, equals minus the tension of the D25-brane (b) Lower-dimensional D-branes are solitonic solutions of the string theory on the back- ground of a D25-brane. (c) The locally stable vacuum of the system is the closed string vac- uum; it has no open string excitations exist. Work in SFT established these conjectures by finding the tachyon vac- uum, first numerically, and then analytically (Schnabl, 2005). These are non-perturbative results. 2 • String field theory is the first complete definition of string pertur- bation theory. The first-quantized world-sheet formulation of string theory does not define string perturbation theory completely: – No systematic way of dealing with IR divergences. – No systematic way of dealing with S-matrix elements for states that undergo mass renormalization. Work of A. Sen and collaborators demonstrating this: (a) One loop-mass renormalization of unstable particles in critical string theories. (b) Fixing ambiguities in two-dimensional string theory: For the one- instanton contribution to N-point scattering amplitudes there are four undetermined constants (Balthazar, Rodriguez, Yin, 2019). Two of them have been fixed with SFT (Sen 2020) (c) Fixing the normalization of Type IIB D-instanton amplitudes (Sen, 2021). -
Chapter 9: the 'Emergence' of Spacetime in String Theory
Chapter 9: The `emergence' of spacetime in string theory Nick Huggett and Christian W¨uthrich∗ May 21, 2020 Contents 1 Deriving general relativity 2 2 Whence spacetime? 9 3 Whence where? 12 3.1 The worldsheet interpretation . 13 3.2 T-duality and scattering . 14 3.3 Scattering and local topology . 18 4 Whence the metric? 20 4.1 `Background independence' . 21 4.2 Is there a Minkowski background? . 24 4.3 Why split the full metric? . 27 4.4 T-duality . 29 5 Quantum field theoretic considerations 29 5.1 The graviton concept . 30 5.2 Graviton coherent states . 32 5.3 GR from QFT . 34 ∗This is a chapter of the planned monograph Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity, co-authored by Nick Huggett and Christian W¨uthrich and under contract with Oxford University Press. More information at www.beyondspacetime.net. The primary author of this chapter is Nick Huggett ([email protected]). This work was sup- ported financially by the ACLS and the John Templeton Foundation (the views expressed are those of the authors not necessarily those of the sponsors). We want to thank Tushar Menon and James Read for exceptionally careful comments on a draft this chapter. We are also grateful to Niels Linnemann for some helpful feedback. 1 6 Conclusions 35 This chapter builds on the results of the previous two to investigate the extent to which spacetime might be said to `emerge' in perturbative string the- ory. Our starting point is the string theoretic derivation of general relativity explained in depth in the previous chapter, and reviewed in x1 below (so that the philosophical conclusions of this chapter can be understood by those who are less concerned with formal detail, and so skip the previous one).