Busstepp Lectures on String Theory
Total Page:16
File Type:pdf, Size:1020Kb
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. -
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. -
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. -
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. -
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]. -
8. Compactification and T-Duality
8. Compactification and T-Duality In this section, we will consider the simplest compactification of the bosonic string: a background spacetime of the form R1,24 S1 (8.1) ⇥ The circle is taken to have radius R, so that the coordinate on S1 has periodicity X25 X25 +2⇡R ⌘ We will initially be interested in the physics at length scales R where motion on the S1 can be ignored. Our goal is to understand what physics looks like to an observer living in the non-compact R1,24 Minkowski space. This general idea goes by the name of Kaluza-Klein compactification. We will view this compactification in two ways: firstly from the perspective of the spacetime low-energy e↵ective action and secondly from the perspective of the string worldsheet. 8.1 The View from Spacetime Let’s start with the low-energy e↵ective action. Looking at length scales R means that we will take all fields to be independent of X25: they are instead functions only on the non-compact R1,24. Consider the metric in Einstein frame. This decomposes into three di↵erent fields 1,24 on R :ametricG˜µ⌫,avectorAµ and a scalar σ which we package into the D =26 dimensional metric as 2 µ ⌫ 2σ 25 µ 2 ds = G˜µ⌫ dX dX + e dX + Aµ dX (8.2) Here all the indices run over the non-compact directions µ, ⌫ =0 ,...24 only. The vector field Aµ is an honest gauge field, with the gauge symmetry descend- ing from di↵eomorphisms in D =26dimensions.Toseethisrecallthatunderthe transformation δXµ = V µ(X), the metric transforms as δG = ⇤ + ⇤ µ⌫ rµ ⌫ r⌫ µ This means that di↵eomorphisms of the compact direction, δX25 =⇤(Xµ), turn into gauge transformations of Aµ, δAµ = @µ⇤ –197– We’d like to know how the fields Gµ⌫, Aµ and σ interact. -
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. -
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. -
What Lattice Theorists Can Do for Superstring/M-Theory
July 26, 2016 0:28 WSPC/INSTRUCTION FILE review˙2016July23 International Journal of Modern Physics A c World Scientific Publishing Company What lattice theorists can do for superstring/M-theory MASANORI HANADA Yukawa Institute for Theoretical Physics Kyoto University, Kyoto 606-8502, JAPAN The Hakubi Center for Advanced Research Kyoto University, Kyoto 606-8501, JAPAN Stanford Institute for Theoretical Physics Stanford University, Stanford, CA 94305, USA [email protected] The gauge/gravity duality provides us with nonperturbative formulation of superstring/M-theory. Although inputs from gauge theory side are crucial for answering many deep questions associated with quantum gravitational aspects of superstring/M- theory, many of the important problems have evaded analytic approaches. For them, lattice gauge theory is the only hope at this moment. In this review I give a list of such problems, putting emphasis on problems within reach in a five-year span, including both Euclidean and real-time simulations. Keywords: Lattice Gauge Theory; Gauge/Gravity Duality; Quantum Gravity. PACS numbers:11.15.Ha,11.25.Tq,11.25.Yb,11.30.Pb Preprint number:YITP-16-28 1. Introduction During the second superstring revolution, string theorists built a beautiful arXiv:1604.05421v2 [hep-lat] 23 Jul 2016 framework for quantum gravity: the gauge/gravity duality.1, 2 It claims that superstring/M-theory is equivalent to certain gauge theories, at least about certain background spacetimes (e.g. black brane background, asymptotically anti de-Sitter (AdS) spacetime). Here the word ‘equivalence’ would be a little bit misleading, be- cause it is not clear how to define string/M-theory nonperturbatively; superstring theory has been formulated based on perturbative expansions, and M-theory3 is defined as the strong coupling limit of type IIA superstring theory, where the non- perturbative effects should play important roles. -
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. -
Refined Topological Branes Arxiv:1805.00993V1 [Hep-Th] 2 May 2018
ITEP-TH-08/18 IITP-TH-06/18 Refined Topological Branes Can Koz¸caza;b;c;1 Shamil Shakirovd;e;f;2 Cumrun Vafac and Wenbin Yang;b;c;3 aDepartment of Physics, Bo˘gazi¸ciUniversity 34342 Bebek, Istanbul, Turkey bCenter of Mathematical Sciences and Applications, Harvard University 20 Garden Street, Cambridge, MA 02138, USA cJefferson Physical Laboratory, Harvard University 17 Oxford Street, Cambridge, MA 02138, USA dSociety of Fellows, Harvard University Cambridge, MA 02138, USA eInstitute for Information Transmission Problems, Moscow 127994, Russia f Mathematical Sciences Research Institute, Berkeley, CA 94720, USA gYau Mathematical Sciences Center, Tsinghua University, Haidian district, Beijing, China, 100084 Abstract: We study the open refined topological string amplitudes using the refined topological vertex. We determine the refinement of holonomies necessary to describe the boundary conditions of open amplitudes (which in particular satisfy the required integrality properties). We also derive the refined holonomies using the refined Chern- Simons theory. arXiv:1805.00993v1 [hep-th] 2 May 2018 1Current affiliation Bo˘gazi¸ciUniversity 2Current affiliation Mathematical Sciences Research Institute 3Current affiliation Yau Mathematical Sciences Center Contents 1 Introduction1 2 Topological Branes3 2.1 External topological branes5 2.2 Internal topological branes7 2.2.1 Topological t-branes8 2.2.2 Topological q-branes 10 3 Topological Branes from refined Chern-Simons Theory 11 3.1 Topological t-branes from refined Chern-Simons theory 13 3.2 Topological q-branes from refined Chern-Simons theory 15 3.3 Duality relation and brane changing operator 15 4 Application: Double compactified toric Calabi-Yau 3-fold 17 4.1 Generic case 19 4.2 Case Qτ = 0 20 4.3 Case Qρ = 0 21 5 Discussion and Outlook 22 A Appenix A: Useful Identities 23 1 Introduction Gauge theories with N = 2 supersymmetry in 4d have been important playground for theoretical physics since the celebrated solution of Seiberg and Witten [1,2].