TASI Lectures on String Compactification, Model Building
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S-Duality in N=1 Orientifold Scfts
S-duality in = 1 orientifold SCFTs N Iñaki García Etxebarria 1210.7799, 1307.1701 with B. Heidenreich and T. Wrase and 1506.03090, 1612.00853, 18xx.xxxxx with B. Heidenreich 3 Intro C =Z3 C(dP 1) General Conclusions Montonen-Olive = 4 (S-)duality N Given a 4d = 4 field theory with gauge group G and gauge N coupling τ = θ + i=g2 (*), there is a completely equivalent description with gauge group G and coupling 1/τ (for θ = 0 this _ − is g 1=g). Examples: $ G G_ U(1) U(1) U(N) U(N) SU(N) SU(N)=ZN SO(2N) SO(2N) SO(2N + 1) Sp(2N) Very non-perturbative duality, exchanges electrically charged operators with magnetically charged ones. (*) I will not describe global structure or line operators here. 3 Intro C =Z3 C(dP 1) General Conclusions S-duality u = 1+iτ j(τ) i+τ j j In this representation τ 1/τ is u u. ! − ! − 3 Intro C =Z3 C(dP 1) General Conclusions S-duality in < 4 N Three main ways of generalizing = 4 S-duality: N Trace what relevant susy-breaking deformations do in different duality frames. [Argyres, Intriligator, Leigh, Strassler ’99]... Make a guess [Seiberg ’94]. Identify some higher principle behind = 4 S-duality, and find backgrounds with less susy that followN the same principle. (2; 0) 6d theory on T 2 Riemann surfaces. [Gaiotto ’09], ..., [Gaiotto, Razamat! ’15], [Hanany, Maruyoshi ’15],... Field theory S-duality from IIB S-duality. 3 Intro C =Z3 C(dP 1) General Conclusions Field theories from solitons One way to construct four dimensional field theories from string theory is to build solitons with a four dimensional core. -
Jhep05(2019)105
Published for SISSA by Springer Received: March 21, 2019 Accepted: May 7, 2019 Published: May 20, 2019 Modular symmetries and the swampland conjectures JHEP05(2019)105 E. Gonzalo,a;b L.E. Ib´a~neza;b and A.M. Urangaa aInstituto de F´ısica Te´orica IFT-UAM/CSIC, C/ Nicol´as Cabrera 13-15, Campus de Cantoblanco, 28049 Madrid, Spain bDepartamento de F´ısica Te´orica, Facultad de Ciencias, Universidad Aut´onomade Madrid, 28049 Madrid, Spain E-mail: [email protected], [email protected], [email protected] Abstract: Recent string theory tests of swampland ideas like the distance or the dS conjectures have been performed at weak coupling. Testing these ideas beyond the weak coupling regime remains challenging. We propose to exploit the modular symmetries of the moduli effective action to check swampland constraints beyond perturbation theory. As an example we study the case of heterotic 4d N = 1 compactifications, whose non-perturbative effective action is known to be invariant under modular symmetries acting on the K¨ahler and complex structure moduli, in particular SL(2; Z) T-dualities (or subgroups thereof) for 4d heterotic or orbifold compactifications. Remarkably, in models with non-perturbative superpotentials, the corresponding duality invariant potentials diverge at points at infinite distance in moduli space. The divergence relates to towers of states becoming light, in agreement with the distance conjecture. We discuss specific examples of this behavior based on gaugino condensation in heterotic orbifolds. We show that these examples are dual to compactifications of type I' or Horava-Witten theory, in which the SL(2; Z) acts on the complex structure of an underlying 2-torus, and the tower of light states correspond to D0-branes or M-theory KK modes. -
String Creation and Heterotic–Type I' Duality
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server hep-th/9711098 HUTP-97/A048 DAMTP-97-119 PUPT-1730 String Creation and Heterotic–Type I’ Duality Oren Bergman a∗, Matthias R. Gaberdiel b† and Gilad Lifschytz c‡ a Lyman Laboratory of Physics Harvard University Cambridge, MA 02138 b Department of Applied Mathematics and Theoretical Physics Cambridge University Silver Street Cambridge, CB3 9EW U. K. c Joseph Henry Laboratories Princeton University Princeton, NJ 08544 November 1997 Abstract The BPS spectrum of type I’ string theory in a generic background is derived using the duality with the nine-dimensional heterotic string theory with Wilson lines. It is shown that the corresponding mass formula has a natural interpretation in terms of type I’, and it is demonstrated that the relevant states in type I’ preserve supersym- metry. By considering certain BPS states for different Wilson lines an independent confirmation of the string creation phenomenon in the D0-D8 system is found. We also comment on the non-perturbative realization of gauge enhancement in type I’, and on the predictions for the quantum mechanics of type I’ D0-branes. ∗E-mail address: [email protected] †E-mail address: [email protected] ‡E-mail address: [email protected] 1 Introduction An interesting phenomenon involving crossing D-branes has recently been discovered [1, 2, 3]. When a Dp-brane and a D(8 − p)-brane that are mutually transverse cross, a fundamental string is created between them. This effect is related by U-duality to the creation of a D3- brane when appropriately oriented Neveu-Schwarz and Dirichlet 5-branes cross [4]. -
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. -
(^Ggy Heterotic and Type II Orientifold Compactifications on SU(3
DE06FA418 DEUTSCHES ELEKTRONEN-SYNCHROTRON (^ggy in der HELMHOLTZ-GEMEINSCHAFT DESY-THESIS-2006-016 July 2006 Heterotic and Type II Orientifold Compactifications on SU(3) Structure Manifolds by I. Benmachiche ISSN 1435-8085 NOTKESTRASSE 85 - 22607 HAMBURG DESY behält sich alle Rechte für den Fall der Schutzrechtserteilung und für die wirtschaftliche Verwertung der in diesem Bericht enthaltenen Informationen vor. DESY reserves all rights for commercial use of information included in this report, especially in case of filing application for or grant of patents. To be sure that your reports and preprints are promptly included in the HEP literature database send them to (if possible by air mail): DESY DESY Zentralbibliothek Bibliothek Notkestraße 85 Platanenallee 6 22607 Hamburg 15738Zeuthen Germany Germany Heterotic and type II orientifold compactifications on SU(3) structure manifolds Dissertation zur Erlangung des Doktorgrades des Departments fur¨ Physik der Universit¨at Hamburg vorgelegt von Iman Benmachiche Hamburg 2006 2 Gutachter der Dissertation: Prof. Dr. J. Louis Jun. Prof. Dr. H. Samtleben Gutachter der Disputation: Prof. Dr. J. Louis Prof. Dr. K. Fredenhagen Datum der Disputation: 11.07.2006 Vorsitzender des Prufungsaussc¨ husses: Prof. Dr. J. Bartels Vorsitzender des Promotionsausschusses: Prof. Dr. G. Huber Dekan der Fakult¨at Mathematik, Informatik und Naturwissenschaften : Prof. Dr. A. Fruh¨ wald Abstract We study the four-dimensional N = 1 effective theories of generic SU(3) structure compactifications in the presence of background fluxes. For heterotic and type IIA/B orientifold theories, the N = 1 characteristic data are determined by a Kaluza-Klein reduction of the fermionic actions. The K¨ahler potentials, superpo- tentials and the D-terms are entirely encoded by geometrical data of the internal manifold. -
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. -
Flux Backgrounds, Ads/CFT and Generalized Geometry Praxitelis Ntokos
Flux backgrounds, AdS/CFT and Generalized Geometry Praxitelis Ntokos To cite this version: Praxitelis Ntokos. Flux backgrounds, AdS/CFT and Generalized Geometry. Physics [physics]. Uni- versité Pierre et Marie Curie - Paris VI, 2016. English. NNT : 2016PA066206. tel-01620214 HAL Id: tel-01620214 https://tel.archives-ouvertes.fr/tel-01620214 Submitted on 20 Oct 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. THÈSE DE DOCTORAT DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Spécialité : Physique École doctorale : « Physique en Île-de-France » réalisée à l’Institut de Physique Thèorique CEA/Saclay présentée par Praxitelis NTOKOS pour obtenir le grade de : DOCTEUR DE L’UNIVERSITÉ PIERRE ET MARIE CURIE Sujet de la thèse : Flux backgrounds, AdS/CFT and Generalized Geometry soutenue le 23 septembre 2016 devant le jury composé de : M. Ignatios ANTONIADIS Examinateur M. Stephano GIUSTO Rapporteur Mme Mariana GRAÑA Directeur de thèse M. Alessandro TOMASIELLO Rapporteur Abstract: The search for string theory vacuum solutions with non-trivial fluxes is of particular importance for the construction of models relevant for particle physics phenomenology. In the framework of the AdS/CFT correspondence, four-dimensional gauge theories which can be considered to descend from N = 4 SYM are dual to ten- dimensional field configurations with geometries having an asymptotically AdS5 factor. -
Lecture Notes on D-Brane Models with Fluxes
Lecture Notes on D-brane Models with Fluxes PoS(RTN2005)001 Ralph Blumenhagen∗ Max-Planck-Institut für Physik, Föhringer Ring 6, D-80805 München, GERMANY E-mail: [email protected] This is a set of lecture notes for the RTN Winter School on Strings, Supergravity and Gauge Theories, January 31-February 4 2005, SISSA/ISAS Trieste. On a basic (inevitably sometimes superficial) level, intended to be suitable for students, recent developments in string model build- ing are covered. This includes intersecting D-brane models, flux compactifications, the KKLT scenario and the statistical approach to the string vacuum problem. RTN Winter School on Strings, Supergravity and Gauge Theories 31/1-4/2 2005 SISSA, Trieste, Italy ∗Speaker. Published by SISSA http://pos.sissa.it/ Lecture Notes on D-brane Models with Fluxes Ralph Blumenhagen Contents 1. D-brane models 2 1.1 Gauge fields on D-branes 3 1.2 Orientifolds 4 1.3 Chirality 6 1.4 T-duality 7 1.5 Intersecting D-brane models 7 2. Flux compactifications 9 PoS(RTN2005)001 2.1 New tadpoles 10 2.2 The scalar potential 11 3. The KKLT scenario 12 3.1 AdS minima 13 3.2 dS minima 13 4. Toward realistic brane and flux compactifications 15 4.1 A supersymmetric G3 flux 15 4.2 MSSM like magnetized D-branes 17 5. Statistics of string vacua 18 1. D-brane models It is still a great challenge for string theory to answer the basic question whether it has anything to do with nature. In the framework of string theory this question boils down to whether string theory incorporates the Standard Model (SM) of particle physics at low energies or whether string theory has a vacuum/vacua resembling our world to the degree of accuracy with which it has been measured. -
Holography and Compactification
PUPT-1872 ITFA-99-14 Holography and Compactification Herman Verlinde Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544 and Institute for Theoretical Physics, University of Amsterdam Valckenierstraat 65, 1018 XE Amsterdam Abstract arXiv:hep-th/9906182v1 24 Jun 1999 Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactifica- tion manifold. A specific example is provided by the type II orientifold equivalent to type I theory on (orbifolds of) T 6, upon taking into account the gravitational backreaction of the D3-branes localized inside the T 6. The conformal factor of the four-dimensional metric depends exponentially on one of the compact directions, which, via the holographic corre- spondence, becomes identified with the renormalization group scale in the uncompactified world. This set-up can be viewed as a generalization of the AdS/CFT correspondence to boundary theories that include gravitational dynamics. A striking consequence is that, in this scenario, the fundamental Planck size string and the large N QCD string appear as (two different wavefunctions of) one and the same object. 1 Introduction In string theory, when considered as a framework for unifying gravity and quantum mechan- ics, the fundamental strings are naturally thought of as Planck size objects. At much lower energies, such as the typical weak or strong interaction scales, the strings have lost all their internal structure and behave just as ordinary point-particles. The physics in this regime is therefore accurately described in terms of ordinary local quantum field theory, decoupled from the planckian realm of all string and quantum gravitational physics. -
Buffy & Angel Watching Order
Start with: End with: BtVS 11 Welcome to the Hellmouth Angel 41 Deep Down BtVS 11 The Harvest Angel 41 Ground State BtVS 11 Witch Angel 41 The House Always Wins BtVS 11 Teacher's Pet Angel 41 Slouching Toward Bethlehem BtVS 12 Never Kill a Boy on the First Date Angel 42 Supersymmetry BtVS 12 The Pack Angel 42 Spin the Bottle BtVS 12 Angel Angel 42 Apocalypse, Nowish BtVS 12 I, Robot... You, Jane Angel 42 Habeas Corpses BtVS 13 The Puppet Show Angel 43 Long Day's Journey BtVS 13 Nightmares Angel 43 Awakening BtVS 13 Out of Mind, Out of Sight Angel 43 Soulless BtVS 13 Prophecy Girl Angel 44 Calvary Angel 44 Salvage BtVS 21 When She Was Bad Angel 44 Release BtVS 21 Some Assembly Required Angel 44 Orpheus BtVS 21 School Hard Angel 45 Players BtVS 21 Inca Mummy Girl Angel 45 Inside Out BtVS 22 Reptile Boy Angel 45 Shiny Happy People BtVS 22 Halloween Angel 45 The Magic Bullet BtVS 22 Lie to Me Angel 46 Sacrifice BtVS 22 The Dark Age Angel 46 Peace Out BtVS 23 What's My Line, Part One Angel 46 Home BtVS 23 What's My Line, Part Two BtVS 23 Ted BtVS 71 Lessons BtVS 23 Bad Eggs BtVS 71 Beneath You BtVS 24 Surprise BtVS 71 Same Time, Same Place BtVS 24 Innocence BtVS 71 Help BtVS 24 Phases BtVS 72 Selfless BtVS 24 Bewitched, Bothered and Bewildered BtVS 72 Him BtVS 25 Passion BtVS 72 Conversations with Dead People BtVS 25 Killed by Death BtVS 72 Sleeper BtVS 25 I Only Have Eyes for You BtVS 73 Never Leave Me BtVS 25 Go Fish BtVS 73 Bring on the Night BtVS 26 Becoming, Part One BtVS 73 Showtime BtVS 26 Becoming, Part Two BtVS 74 Potential BtVS 74 -
Introduction to String Theory
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Introduction to String Theory Thomas Mohaupt Friedrich-Schiller Universit¨at Jena, Max-Wien-Platz 1, D-07743 Jena, Germany Abstract. We give a pedagogical introduction to string theory, D-branes and p-brane solutions. 1 Introductory remarks These notes are based on lectures given at the 271-th WE-Haereus-Seminar ‘Aspects of Quantum Gravity’. Their aim is to give an introduction to string theory for students and interested researches. No previous knowledge of string theory is assumed. The focus is on gravitational aspects and we explain in some detail how gravity is described in string theory in terms of the graviton excitation of the string and through background gravitational fields. We include Dirichlet boundary conditions and D-branes from the beginning and devote one section to p-brane solutions and their relation to D-branes. In the final section we briefly indicate how string theory fits into the larger picture of M-theory and mention some of the more recent developments, like brane world scenarios. The WE-Haereus-Seminar ‘Aspects of Quantum Gravity’ covered both main approaches to quantum gravity: string theory and canonical quantum gravity. Both are complementary in many respects. While the canonical approach stresses background independence and provides a non-perturbative framework, the cor- nerstone of string theory still is perturbation theory in a fixed background ge- ometry. Another difference is that in the canonical approach gravity and other interactions are independent from each other, while string theory automatically is a unified theory of gravity, other interactions and matter. -
Mathematically Talented Women in Hollywood: Fred in Angel
Mathematically Talented Women in Hollywood: Fred in Angel Sarah J. Greenwald and Jill E. Thomley Appalachian State University Introduction Individual faculty such as those represented in this volume have used popular culture in the class- room to alleviate math anxiety and to help students connect to significant mathematics. Recent educational initiatives such as We All Use Math Every Day [12], co-sponsored by CBS, Texas In- struments, and the National Council of Teachers of Mathematics, and MathMovesU [31], sponsored by Raytheon, strive to change attitudes and attract students to mathematics by capitalizing on student enjoyment of celebrities and popular culture. At the same time, Hollywood has increased its use of math and mathematicians, but some of those representations may not be all that positive for attracting students to mathematics. Others have examined the stereotype of the mentally ill mathematician (e.g., [25]), which may make it harder for students to identify with mathematicians. In this article we discuss the representations of mathematically talented women in Hollywood and provide a framework for examining the messages they may convey to the public and our students as we examine the example of physicist Fred Burkle in the television show Angel [1]. Unlike more recent representations of women mathematicians, such as Amita in NUMB3RS, which are aimed at a more mature audience, Angel aired on the WB network from October 1999 to May 2004 as part of a lineup of programs specifically targeted at teens and young adults. It is for this reason, and also because Fred’s experiences provide a rich context to discuss a variety of issues related to women in mathematics, that we chose Fred as a case study.