Free Lunch from T-Duality
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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. -
ABSTRACT Investigation Into Compactified Dimensions: Casimir
ABSTRACT Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects Richard K. Obousy, Ph.D. Chairperson: Gerald B. Cleaver, Ph.D. The primary focus of this dissertation is the study of the Casimir effect and the possibility that this phenomenon may serve as a mechanism to mediate higher dimensional stability, and also as a possible mechanism for creating a small but non- zero vacuum energy density. In chapter one we review the nature of the quantum vacuum and discuss the different contributions to the vacuum energy density arising from different sectors of the standard model. Next, in chapter two, we discuss cosmology and the introduction of the cosmological constant into Einstein's field equations. In chapter three we explore the Casimir effect and study a number of mathematical techniques used to obtain a finite physical result for the Casimir energy. We also review the experiments that have verified the Casimir force. In chapter four we discuss the introduction of extra dimensions into physics. We begin by reviewing Kaluza Klein theory, and then discuss three popular higher dimensional models: bosonic string theory, large extra dimensions and warped extra dimensions. Chapter five is devoted to an original derivation of the Casimir energy we derived for the scenario of a higher dimensional vector field coupled to a scalar field in the fifth dimension. In chapter six we explore a range of vacuum scenarios and discuss research we have performed regarding moduli stability. Chapter seven explores a novel approach to spacecraft propulsion we have proposed based on the idea of manipulating the extra dimensions of string/M theory. -
Arxiv:2007.12543V4 [Hep-Th] 15 Mar 2021 Contents
Jacobi sigma models F. Basconea;b Franco Pezzellaa Patrizia Vitalea;b aINFN - Sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, 80126 Napoli, Italy bDipartimento di Fisica “E. Pancini”, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, 80126 Napoli, Italy E-mail: [email protected], [email protected], [email protected] Abstract: We introduce a two-dimensional sigma model associated with a Jacobi mani- fold. The model is a generalisation of a Poisson sigma model providing a topological open string theory. In the Hamiltonian approach first class constraints are derived, which gen- erate gauge invariance of the model under diffeomorphisms. The reduced phase space is finite-dimensional. By introducing a metric tensor on the target, a non-topological sigma model is obtained, yielding a Polyakov action with metric and B-field, whose target space is a Jacobi manifold. Keywords: Sigma Models, Topological Strings arXiv:2007.12543v4 [hep-th] 15 Mar 2021 Contents 1 Introduction1 2 Poisson sigma models3 3 Jacobi sigma models5 3.1 Jacobi brackets and Jacobi manifold5 3.1.1 Homogeneous Poisson structure on M × R from Jacobi structure7 3.2 Poisson sigma model on M × R 7 3.3 Action principle on the Jacobi manifold8 3.3.1 Hamiltonian description, constraints and gauge transformations9 4 Metric extension and Polyakov action 15 5 Jacobi sigma model on SU(2) 16 6 Conclusions and Outlook 18 1 Introduction Jacobi sigma models are here introduced as a natural generalisation of Poisson sigma mod- els. -
Gauged Sigma Models and Magnetic Skyrmions Abstract Contents
SciPost Phys. 7, 030 (2019) Gauged sigma models and magnetic Skyrmions Bernd J. Schroers Maxwell Institute for Mathematical Sciences and Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, UK [email protected] Abstract We define a gauged non-linear sigma model for a 2-sphere valued field and a SU(2) connection on an arbitrary Riemann surface whose energy functional reduces to that for critically coupled magnetic skyrmions in the plane, with arbitrary Dzyaloshinskii-Moriya interaction, for a suitably chosen gauge field. We use the interplay of unitary and holo- morphic structures to derive a general solution of the first order Bogomol’nyi equation of the model for any given connection. We illustrate this formula with examples, and also point out applications to the study of impurities. Copyright B. J. Schroers. Received 23-05-2019 This work is licensed under the Creative Commons Accepted 28-08-2019 Check for Attribution 4.0 International License. Published 10-09-2019 updates Published by the SciPost Foundation. doi:10.21468/SciPostPhys.7.3.030 Contents 1 Introduction1 2 Gauged sigma models on a Riemann surface3 2.1 Conventions3 2.2 Energy and variational equations4 2.3 The Bogomol’nyi equation5 2.4 Boundary terms6 3 Solving the Bogomol’nyi equation7 3.1 Holomorphic versus unitary structures7 3.2 Holomorphic structure of the gauged sigma model9 3.3 A general solution 11 4 Applications to magnetic skyrmions and impurities 12 4.1 Critically coupled magnetic skyrmions with any DM term 12 4.2 Axisymmetric DM interactions 13 4.3 Rank one DM interaction 15 4.4 Impurities as non-abelian gauge fields 16 5 Conclusion 17 References 18 1 SciPost Phys. -
D-Branes in Topological Membranes
OUTP/03–21P HWM–03–14 EMPG–03–13 hep-th/0308101 August 2003 D-BRANES IN TOPOLOGICAL MEMBRANES P. Castelo Ferreira Dep. de Matem´atica – Instituto Superior T´ecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal and PACT – University of Sussex, Falmer, Brighton BN1 9QJ, U.K. [email protected] I.I. Kogan Dept. of Physics, Theoretical Physics – University of Oxford, Oxford OX1 3NP, U.K. R.J. Szabo Dept. of Mathematics – Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K. [email protected] Abstract arXiv:hep-th/0308101v1 15 Aug 2003 It is shown how two-dimensional states corresponding to D-branes arise in orbifolds of topologically massive gauge and gravity theories. Brane vertex operators naturally appear in induced worldsheet actions when the three-dimensional gauge theory is minimally coupled to external charged matter and the orbifold relations are carefully taken into account. Boundary states corresponding to D-branes are given by vacuum wavefunctionals of the gauge theory in the presence of the matter, and their various constraints, such as the Cardy condition, are shown to arise through compatibility relations between the orbifold charges and bulk gauge invariance. We show that with a further conformally-invariant coupling to a dynamical massless scalar field theory in three dimensions, the brane tension is naturally set by the bulk mass scales and arises through dynamical mechanisms. As an auxilliary result, we show how to describe string descendent states in the three-dimensional theory through the construction of gauge-invariant excited wavefunctionals. Contents 1 INTRODUCTION AND SUMMARY 1 1.1 D-Branes .................................... -
Universit`A Degli Studi Di Padova
UNIVERSITA` DEGLI STUDI DI PADOVA Dipartimento di Fisica e Astronomia “Galileo Galilei” Corso di Laurea Magistrale in Fisica Tesi di Laurea Finite symmetry groups and orbifolds of two-dimensional toroidal conformal field theories Relatore Laureando Prof. Roberto Volpato Tommaso Macrelli Anno Accademico 2017/2018 Contents Introduction 5 1 Introduction to two dimensional Conformal Field Theory 7 1.1 The conformal group . .7 1.1.1 Conformal group in two dimensions . .9 1.2 Conformal invariance in two dimensions . 12 1.2.1 Fields and correlation functions . 12 1.2.2 Stress-energy tensor and conformal transformations . 13 1.2.3 Operator formalism: radial quantization . 14 1.3 General structure of a Conformal Field Theory in two dimensions . 16 1.3.1 Meromorphic Conformal Field Theory . 18 1.4 Examples . 22 1.4.1 Free boson . 22 1.4.2 Free Majorana fermion . 26 1.4.3 Ghost system . 27 2 Elements of String and Superstring Theory 28 2.1 Bosonic String Theory . 29 2.1.1 Classical Bosonic String . 29 2.1.2 Quantization . 31 2.1.3 BRST symmetry and Hilbert Space . 33 2.1.4 Spectrum of the Bosonic String . 34 2.1.5 What’s wrong with Bosonic String? . 36 2.2 Superstring Theory . 37 2.2.1 Introduction to Superstrings . 37 2.2.2 Heterotic String . 39 3 Compactifications of String Theory 41 3.1 An introduction: Kaluza-Klein compactification . 42 3.2 Free boson compactified on a circle . 43 3.2.1 Closed strings and T-Duality . 45 3.2.2 Enhanced symmetries at self-dual radius . -
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. -
String Field Theory, Nucl
1 String field theory W. TAYLOR MIT, Stanford University SU-ITP-06/14 MIT-CTP-3747 hep-th/0605202 Abstract This elementary introduction to string field theory highlights the fea- tures and the limitations of this approach to quantum gravity as it is currently understood. String field theory is a formulation of string the- ory as a field theory in space-time with an infinite number of massive fields. Although existing constructions of string field theory require ex- panding around a fixed choice of space-time background, the theory is in principle background-independent, in the sense that different back- grounds can be realized as different field configurations in the theory. String field theory is the only string formalism developed so far which, in principle, has the potential to systematically address questions involv- ing multiple asymptotically distinct string backgrounds. Thus, although it is not yet well defined as a quantum theory, string field theory may eventually be helpful for understanding questions related to cosmology arXiv:hep-th/0605202v2 28 Jun 2006 in string theory. 1.1 Introduction In the early days of the subject, string theory was understood only as a perturbative theory. The theory arose from the study of S-matrices and was conceived of as a new class of theory describing perturbative interactions of massless particles including the gravitational quanta, as well as an infinite family of massive particles associated with excited string states. In string theory, instead of the one-dimensional world line 1 2 W. Taylor of a pointlike particle tracing out a path through space-time, a two- dimensional surface describes the trajectory of an oscillating loop of string, which appears pointlike only to an observer much larger than the string. -
String Theory on Ads3 and the Symmetric Orbifold of Liouville Theory
Prepared for submission to JHEP String theory on AdS3 and the symmetric orbifold of Liouville theory Lorenz Eberhardt and Matthias R. Gaberdiel Institut f¨urTheoretische Physik, ETH Zurich, CH-8093 Z¨urich,Switzerland E-mail: [email protected], [email protected] Abstract: For string theory on AdS3 with pure NS-NS flux a complete set of DDF operators is constructed, from which one can read off the symmetry algebra of the spacetime CFT. Together with an analysis of the spacetime spectrum, this allows 3 4 us to show that the CFT dual of superstring theory on AdS3 × S × T for generic NS-NS flux is the symmetric orbifold of (N = 4 Liouville theory) × T4. For the case of minimal flux (k = 1), the Liouville factor disappears, and we just obtain the symmetric orbifold of T4, thereby giving further support to a previous claim. We also show that a similar analysis can be done for bosonic string theory on AdS3 × X. arXiv:1903.00421v1 [hep-th] 1 Mar 2019 Contents 1 Introduction1 2 Bosonic strings on AdS3 3 2.1 The sl(2; R)k WZW model and its free field realisation3 2.2 Vertex operators4 2.3 The DDF operators5 2.4 The identity operator8 2.5 The moding of the spacetime algebra8 2.6 Identifying Liouville theory on the world-sheet 11 2.7 Discrete representations 13 3 4 3 A review of superstrings on AdS3 × S × T 15 3.1 The RNS formalism 15 3.2 The hybrid formalism 17 3.3 Supergroup generators 18 4 The psu(1; 1j2)k WZW model 19 4.1 Wakimoto representation of sl(2; R)k+2 and vertex operators 19 4.2 The short representation 20 4.3 Spectral -
The Grassmannian Sigma Model in SU(2) Yang-Mills Theory
The Grassmannian σ-model in SU(2) Yang-Mills Theory David Marsh Undergraduate Thesis Supervisor: Antti Niemi Department of Theoretical Physics Uppsala University Contents 1 Introduction 4 1.1 Introduction ............................ 4 2 Some Quantum Field Theory 7 2.1 Gauge Theories .......................... 7 2.1.1 Basic Yang-Mills Theory ................. 8 2.1.2 Faddeev, Popov and Ghosts ............... 10 2.1.3 Geometric Digression ................... 14 2.2 The nonlinear sigma models .................. 15 2.2.1 The Linear Sigma Model ................. 15 2.2.2 The Historical Example ................. 16 2.2.3 Geometric Treatment ................... 17 3 Basic properties of the Grassmannian 19 3.1 Standard Local Coordinates ................... 19 3.2 Plücker coordinates ........................ 21 3.3 The Grassmannian as a homogeneous space .......... 23 3.4 The complexied four-vector ................... 25 4 The Grassmannian σ Model in SU(2) Yang-Mills Theory 30 4.1 The SU(2) Yang-Mills Theory in spin-charge separated variables 30 4.1.1 Variables .......................... 30 4.1.2 The Physics of Spin-Charge Separation ......... 34 4.2 Appearance of the ostensible model ............... 36 4.3 The Grassmannian Sigma Model ................ 38 4.3.1 Gauge Formalism ..................... 38 4.3.2 Projector Formalism ................... 39 4.3.3 Induced Metric Formalism ................ 40 4.4 Embedding Equations ...................... 43 4.5 Hodge Star Decomposition .................... 48 2 4.6 Some Complex Dierential Geometry .............. 50 4.7 Quaternionic Decomposition ................... 54 4.7.1 Verication ........................ 56 5 The Interaction 58 5.1 The Interaction Terms ...................... 58 5.1.1 Limits ........................... 59 5.2 Holomorphic forms and Dolbeault Cohomology ........ 60 5.3 The Form of the interaction .................. -
Introduction to Superstring Theory
Introduction to Superstring theory Carmen Nunez Instituto de Astronomia y Física del Espacio C.C. 67 - Sue. 28, 1428 Buenos Aires, Argentina and Physics Department, University of Buenos Aires [email protected] Abstract 1 Overview The bosonic string theory, despite all its beautiful features, has a number of short comings. The most obvious of these are the absence of fermions and the presence of tachyons in spacetime. The tachyon is not an actual physical inconsistency; it indicates at least that the calculations are being performed in an unstable vacuum state. More over, tachyon exchange contributes infrarred divergences in loop diagrams and these divergences make it hard to isolate the ultraviolet behaviour of the "unified quan tum theory" the bosonic string theory gives rise to and determine whether it is really satisfactory. Historically, the solution to the tachyon problem appeared with the solution to the other problem, the absence of fermions. The addition of a new ingredient, supersym- metry on the world-sheet, improves substantially the general picture. In 1977 Gliozzi, Scherk and Olive showed that it was possible to get a model with no tachyons and with equal masses and multiplicities for bosons and fermions. In 1980, Green and Schwarz proved that this model had spacetime supersymmetry. In the completely consisten- t tachyon free form of the superstring theory it was then possible to show that the one-loop diagrams were completely finite and free of ultraviolet divergences. While most workers on the subject believe that the finiteness will also hold to all orders of perturbation theory, complete and universally accepted proofs have not appeared so far. -
T-Duality Invariant Approaches to String Theory Thompson, Daniel C
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Queen Mary Research Online T-duality invariant approaches to string theory Thompson, Daniel C. The copyright of this thesis rests with the author and no quotation from it or information derived from it may be published without the prior written consent of the author For additional information about this publication click this link. https://qmro.qmul.ac.uk/jspui/handle/123456789/390 Information about this research object was correct at the time of download; we occasionally make corrections to records, please therefore check the published record when citing. For more information contact [email protected] T-duality Invariant Approaches to String Theory Daniel C. Thompsony A thesis submitted for the degree of Doctor of Philosophy y Centre for Research in String Theory, Department of Physics Queen Mary University of London Mile End Road, London E1 4NS, UK Abstract This thesis investigates the quantum properties of T-duality invariant formalisms of String Theory. We introduce and review duality invariant formalisms of String Theory including the Doubled Formalism. We calculate the background field equations for the Doubled Formalism of Abelian T-duality and show how they are consistent with those of a conventional String Theory description of a toroidal compactification. We generalise these considerations to the case of Poisson{Lie T-duality and show that the system of renormalisation group equations obtained from the duality invariant parent theory are equivalent to those of either of the T-dual pair of sigma-models. In duality invariant formalisms it is quite common to loose manifest Lorentz invariance at the level of the Lagrangian.