Calabi-Yau Threefolds and Heterotic String Compactification
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Wall Crossing and M-Theory
Wall Crossing and M-theory The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Aganagic, Mina, Hirosi Ooguri, Cumrun Vafa, and Masahito Yamazaki. 2011. Wall crossing and M-theory. Publications of the Research Institute for Mathematical Sciences 47(2): 569-584. Published Version doi:10.2977/PRIMS/44 Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:7561260 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP CALT-68-2746 IPMU09-0091 UT-09-18 Wall Crossing and M-Theory Mina Aganagic1, Hirosi Ooguri2,3, Cumrun Vafa4 and Masahito Yamazaki2,3,5 1Center for Theoretical Physics, University of California, Berkeley, CA 94720, USA 2California Institute of Technology, Pasadena, CA 91125, USA 3 IPMU, University of Tokyo, Chiba 277-8586, Japan 4Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA 5Department of Physics, University of Tokyo, Tokyo 113-0033, Japan Abstract arXiv:0908.1194v1 [hep-th] 8 Aug 2009 We study BPS bound states of D0 and D2 branes on a single D6 brane wrapping a Calabi- Yau 3-fold X. When X has no compact 4-cyles, the BPS bound states are organized into a free field Fock space, whose generators correspond to BPS states of spinning M2 branes in M- theory compactified down to 5 dimensions by a Calabi-Yau 3-fold X. -
Abdus Salam Educational, Scientific and Cultural XA0500266 Organization International Centre
the united nations abdus salam educational, scientific and cultural XA0500266 organization international centre international atomic energy agency for theoretical physics 1 a M THEORY AND SINGULARITIES OF EXCEPTIONAL HOLONOMY MANIFOLDS Bobby S. Acharya and Sergei Gukov Available at: http://www.ictp.it/-pub-off IC/2004/127 HUTP-03/A053 RUNHETC-2003-26 United Nations Educational Scientific and Cultural Organization and International Atomic Energy Agency THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS M THEORY AND SINGULARITIES OF EXCEPTIONAL HOLONOMY MANIFOLDS Bobby S. Acharya1 The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy and Sergei Gukov2 Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA. Abstract M theory compactifications on Gi holonomy manifolds, whilst supersymmetric, require sin- gularities in order to obtain non-Abelian gauge groups, chiral fermions and other properties necessary for a realistic model of particle physics. We review recent progress in understanding the physics of such singularities. Our main aim is to describe the techniques which have been used to develop our understanding of M theory physics near these singularities. In parallel, we also describe similar sorts of singularities in Spin(7) holonomy manifolds which correspond to the properties of three dimensional field theories. As an application, we review how various aspects of strongly coupled gauge theories, such as confinement, mass gap and non-perturbative phase transitions may be given a -
Heterotic String Compactification with a View Towards Cosmology
Heterotic String Compactification with a View Towards Cosmology by Jørgen Olsen Lye Thesis for the degree Master of Science (Master i fysikk) Department of Physics Faculty of Mathematics and Natural Sciences University of Oslo May 2014 Abstract The goal is to look at what constraints there are for the internal manifold in phe- nomenologically viable Heterotic string compactification. Basic string theory, cosmology, and string compactification is sketched. I go through the require- ments imposed on the internal manifold in Heterotic string compactification when assuming vanishing 3-form flux, no warping, and maximally symmetric 4-dimensional spacetime with unbroken N = 1 supersymmetry. I review the current state of affairs in Heterotic moduli stabilisation and discuss merging cosmology and particle physics in this setup. In particular I ask what additional requirements this leads to for the internal manifold. I conclude that realistic manifolds on which to compactify in this setup are severely constrained. An extensive mathematics appendix is provided in an attempt to make the thesis more self-contained. Acknowledgements I would like to start by thanking my supervier Øyvind Grøn for condoning my hubris and for giving me free rein to delve into string theory as I saw fit. It has lead to a period of intense study and immense pleasure. Next up is my brother Kjetil, who has always been a good friend and who has been constantly looking out for me. It is a source of comfort knowing that I can always turn to him for help. Mentioning friends in such an acknowledgement is nearly mandatory. At least they try to give me that impression. -
Vincent Bouchard – Associate Professor
Vincent Bouchard | Associate Professor Rhodes Scholar (Québec and Magdalen, 2001) Department of Mathematical and Statistical Sciences, University of Alberta 632 CAB, Edmonton, AB, Canada – T6G 2G1 T +1 (780) 492 0099 • B [email protected] Í www.ualberta.ca/ vbouchar Education University of Oxford, Magdalen College Oxford, UK D.Phil. Mathematics 2001–2005 Université de Montréal Montréal, QC B.Sc. Physics, Excellence, Palmarès de la doyenne, average 4.3/4.3 1998–2001 Cégep Saint-Jean-sur-Richelieu Saint-Jean-sur-Richelieu, QC D.E.C. Natural Sciences, Excellence 1996–1998 D.Phil. thesis Title: Toric Geometry and String Theory [arXiv:hep-th/0609123] Supervisor: Rouse Ball Professor Philip Candelas Positions Associate Professor Edmonton, AB Department of Mathematical and Statistical Sciences, University of Alberta 2013–Present Assistant Professor Edmonton, AB Department of Mathematical and Statistical Sciences, University of Alberta 2009–2013 Postdoctoral Fellow Cambridge, MA Physics Department, Harvard University 2007–2009 NSERC Postdoctoral Fellow Waterloo, ON Perimeter Institute for Theoretical Physics 2006–2007 Postdoctoral Fellow Berkeley, CA Mathematical Sciences Research Institute 2006 “New Topological Structures in Physics” program, January–May Postdoctoral Fellow Phildelphia, PA Department of Mathematics, University of Pennsylvania 2005 Joint math/physics visiting position, September–December Research Grants NSERC Discovery Grant: $225,000 2013–2018 NSERC Discovery Grant: $130,000 2010–2013 University of Alberta Research -
Open Gromov-Witten Invariants and Syz Under Local Conifold Transitions
OPEN GROMOV-WITTEN INVARIANTS AND SYZ UNDER LOCAL CONIFOLD TRANSITIONS SIU-CHEONG LAU Abstract. For a local non-toric Calabi-Yau manifold which arises as smoothing of a toric Gorenstein singularity, this paper derives the open Gromov-Witten invariants of a generic fiber of the special Lagrangian fibration constructed by Gross and thereby constructs its SYZ mirror. Moreover it proves that the SYZ mirrors and disc potentials vary smoothly under conifold transitions, giving a global picture of SYZ mirror symmetry. 1. Introduction Let N be a lattice and P a lattice polytope in NR. It is an interesting classical problem in combinatorial geometry to construct Minkowski decompositions of P . P v On the other hand, consider the family of polynomials v2P \N cvz for cv 2 C with cv 6= 0 when v is a vertex of P . All these polynomials have P as their Newton polytopes. This establishes a relation between geometry and algebra, and the geometric problem of finding Minkowski decompositions is transformed to the algebraic problem of finding polynomial factorizations. One purpose of this paper is to show that the beautiful algebro-geometric correspondence between Minkowski decompositions and polynomial factorizations can be realized via SYZ mirror symmetry. A key step leading to the miracle is brought by a result of Altmann [3]. First of all, a lattice polytope corresponds to a toric Gorenstein singularity X. Altmann showed that Minkowski decompositions of the lattice polytope correspond to (partial) smoothings of X. From string- theoretic point of view different smoothings of X belong to different sectors of the same stringy K¨ahlermoduli. -
Singlet Glueballs in Klebanov-Strassler Theory
Singlet Glueballs In Klebanov-Strassler Theory A DISSERTATION SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF THE UNIVERSITY OF MINNESOTA BY IVAN GORDELI IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy ARKADY VAINSHTEIN April, 2016 c IVAN GORDELI 2016 ALL RIGHTS RESERVED Acknowledgements First of all I would like to thank my scientific adviser - Arkady Vainshtein for his incredible patience and support throughout the course of my Ph.D. program. I would also like to thank my committee members for taking time to read and review my thesis, namely Ronald Poling, Mikhail Shifman and Alexander Voronov. I am deeply grateful to Vasily Pestun for his support and motivation. Same applies to my collaborators Dmitry Melnikov and Anatoly Dymarsky who have suggested this research topic to me. I am thankful to my other collaborator - Peter Koroteev. I would like to thank Emil Akhmedov, A.Yu. Morozov, Andrey Mironov, M.A. Olshanetsky, Antti Niemi, K.A. Ter-Martirosyan, M.B. Voloshin, Andrey Levin, Andrei Losev, Alexander Gorsky, S.M. Kozel, S.S. Gershtein, M. Vysotsky, Alexander Grosberg, Tony Gherghetta, R.B. Nevzorov, D.I. Kazakov, M.V. Danilov, A. Chervov and all other great teachers who have shaped everything I know about Theoretical Physics. I am deeply grateful to all my friends and colleagues who have contributed to discus- sions and supported me throughout those years including A. Arbuzov, L. Kushnir, K. Kozlova, A. Shestov, V. Averina, A. Talkachova, A. Talkachou, A. Abyzov, V. Poberezh- niy, A. Alexandrov, G. Nozadze, S. Solovyov, A. Zotov, Y. Chernyakov, N. -
Calabi-Yau Geometry and Higher Genus Mirror Symmetry
Calabi-Yau Geometry and Higher Genus Mirror Symmetry A dissertation presented by Si Li to The Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Mathematics Harvard University Cambridge, Massachusetts May 2011 © 2011 { Si Li All rights reserved. iii Dissertation Advisor: Professor Shing-Tung Yau Si Li Calabi-Yau Geometry and Higher Genus Mirror Symmetry Abstract We study closed string mirror symmetry on compact Calabi-Yau manifolds at higher genus. String theory predicts the existence of two sets of geometric invariants, from the A-model and the B-model on Calabi-Yau manifolds, each indexed by a non-negative inte- ger called genus. The A-model has been mathematically established at all genera by the Gromov-Witten theory, but little is known in mathematics for B-model beyond genus zero. We develop a mathematical theory of higher genus B-model from perturbative quantiza- tion techniques of gauge theory. The relevant gauge theory is the Kodaira-Spencer gauge theory, which is originally discovered by Bershadsky-Cecotti-Ooguri-Vafa as the closed string field theory of B-twisted topological string on Calabi-Yau three-folds. We generalize this to Calabi-Yau manifolds of arbitrary dimensions including also gravitational descen- dants, which we call BCOV theory. We give the geometric description of the perturbative quantization of BCOV theory in terms of deformation-obstruction theory. The vanishing of the relevant obstruction classes will enable us to construct the higher genus B-model. We carry out this construction on the elliptic curve and establish the corresponding higher genus B-model. -
String Cosmology
��������� � ������ ������ �� ��������� ��� ������������� ������� �� � �� ���� ���� ������ ��������� ���� � �� ������� ���������� �� �������� ���������� �� ������� ��������� �� ���������� ������ Lecture 2 Stabilization of moduli in superstring theory Fluxes NS (perturbative string theory) RR (non-perturbative string theory) Non-perturbative corrections to superpotential and Kahler potential Start 2008 Higgs?Higgs? MSSM?MSSM? SplitSplit susysusy?? NoNo susysusy?? IFIF SUSYSUSY ISIS THERETHERE…… The significance of discovery of supersymmetry in nature, which will manifests itself via existence of supersymmetric particles, would be a discovery of the fermionicfermionic dimensionsdimensions ofof spacetimespacetime ItIt willwill bebe thethe mostmost fundamentalfundamental discoverydiscovery inin physicsphysics afterafter EinsteinEinstein’’ss relativityrelativity SUPERSYMMETRY: GravityGravity Supergravity/StringSupergravity/String theorytheory There are no single scalars fields in susy models! Scalars come in pairs, they are always complex in supersymmetry. For example, axion and dilaton or axion and radial modulus. Generically, multi-dimensional moduli space. An effective inflaton may be a particular direction in moduli space. In string theory scalars often have geometrical meaning: distance between branes, size of internal dimensions, size of supersymmetric cycles on which branes can be wrapped, etc StabilizationStabilization ofof modulimoduli isis necessarynecessary forfor stringstring theorytheory toto describedescribe thethe effectiveeffective -
Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7
INSTITUTE OF PHYSICS PUBLISHING CLASSICAL AND QUANTUM GRAVITY Class. Quantum Grav. 20 (2003) 665–705 PII: S0264-9381(03)53801-1 Conifold transitions and five-brane condensation in M-theory on Spin(7) manifolds Sergei Gukov1,JamesSparks2 and David Tong3 1 Jefferson Physical Laboratory, Harvard University, Cambridge, MA 02138, USA 2 Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK 3 Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA E-mail: [email protected], [email protected] and [email protected] Received 23 September 2002, in final form 6 January 2003 Published 28 January 2003 Online at stacks.iop.org/CQG/20/665 Abstract We conjecture a topology-changing transition in M-theory on a non-compact asymptotically conical Spin(7) manifold, where a 5-sphere collapses and a CP2 bolt grows. We argue that the transition may be understood as the condensation of M5-branes wrapping S5.Upon reduction to ten dimensions, it has a physical interpretation as a transition of D6-branes lying on calibrated submanifolds of flat space. In yet another guise, it may be seen as a geometric transition between two phases of type IIA string theory on a G2 holonomy manifold with either wrapped D6-branes, or background Ramond–Ramond flux. This is the first non-trivial example of a topology-changing transition with only 1/16 supersymmetry. PACS numbers: 11.25.Mj, 11.30.Pb, 11.15.Tk Contents 1. Introduction 666 2. D6-branes, M-theory and Spin(7) conifolds 670 2.1. -
Gauss-Manin Connection in Disguise: Calabi-Yau Threefolds 1
Gauss-Manin connection in disguise: Calabi-Yau threefolds 1 Murad Alim, Hossein Movasati, Emanuel Scheidegger, Shing-Tung Yau Abstract We describe a Lie Algebra on the moduli space of Calabi-Yau threefolds enhanced with differential forms and its relation to the Bershadsky-Cecotti-Ooguri-Vafa holo- morphic anomaly equation. In particular, we describe algebraic topological string alg partition functions Fg , g ≥ 1, which encode the polynomial structure of holomorphic and non-holomorphic topological string partition functions. Our approach is based on Grothendieck’s algebraic de Rham cohomology and on the algebraic Gauss-Manin connection. In this way, we recover a result of Yamaguchi-Yau and Alim-L¨ange in an algebraic context. Our proofs use the fact that the special polynomial generators defined using the special geometry of deformation spaces of Calabi-Yau threefolds cor- respond to coordinates on such a moduli space. We discuss the mirror quintic as an example. Contents 1 Introduction 2 2 Holomorphic anomaly equations 7 2.1 Specialgeometry ................................. 7 2.2 Specialcoordinates.............................. 8 2.3 Holomorphic anomaly equations . ... 9 2.4 Polynomialstructure. .. .. .. .. .. .. .. .. 9 3 Algebraic structure of topological string theory 10 3.1 Specialpolynomialrings . 10 3.2 Different choices of Hodge filtrations . ..... 12 3.3 LieAlgebradescription . 13 3.4 Algebraic master anomaly equation . ..... 14 arXiv:1410.1889v1 [math.AG] 7 Oct 2014 4 Proofs 15 4.1 Generalizedperioddomain . 15 4.2 ProofofTheorem1................................ 16 4.3 ProofofTheorem2................................ 17 4.4 The Lie Algebra G ................................ 18 4.5 Two fundamental equalities of the special geometry . .......... 18 5 Mirror quintic case 19 6 Final remarks 21 1 Math. -
MEMORIA DEL CENTRO DE CIENCIAS DE BENASQUE Barcelona, 31 De Diciembre De 2005
MEMORIA DEL CENTRO DE CIENCIAS DE BENASQUE Barcelona, 31 de Diciembre de 2005 I – INTRODUCCIÓN En unos pocos años España se ha convertido en uno de los focos mundiales de atracción de actividades veraniegas, principalmente de carácter lúdico y turístico. Hasta este momento se han usado poco las características de nuestro país para convertirlo en un foco de actividades de tipo científico. Hace unas pocas décadas la representación española en el concierto científico internacional era, prácticamente, inexistente. Aún en 1977 sólo el 0.64% de los artículos científicos que aparecían en la base de datos del Science Citation Index (SCI) tenían algún autor español. En el período 1977-1993 los artículos científicos del SCI en los que al menos un autor era español ha aumentado a un ritmo superior al 9% anual y en 1993 un 2.0% de todos los artículos contenidos en el SCI tienen, al menos, un autor español. Se ha avanzado mucho en pocos años, pero este esfuerzo debe continuar. En España era habitual, en 1994, la celebración de conferencias científicas sobre distintas temáticas y con características diversas. Todas estas reuniones, más o menos multitudinarias, se caracterizan por su corta duración (alrededor de una semana) y gran número diario de conferencias, lo cual hace que quede poco tiempo para poder trabajar o discutir con otros científicos. Sin embargo ni en nuestro país ni en el resto de Europa existían, por aquel entonces, verdaderos centros donde, en un ambiente agradable, los científicos se pudieran dedicar a trabajar tranquilamente y a discutir con sus colegas. Un centro de este tipo lleva muchos años funcionando, con gran éxito, en la localidad norteamericana de Aspen, en Colorado. -
Critical Non-Abelian Vortex in Four Dimensions and Little String Theory
FTPI-MINN-17/06, UMN-TH-3622/17 Critical Non-Abelian Vortex in Four Dimensions and Little String Theory M. Shifman a and A. Yung a,b,c aWilliam I. Fine Theoretical Physics Institute, University of Minnesota, Minneapolis, MN 55455 bNational Research Center “Kurchatov Institute”, Petersburg Nuclear Physics Institute, Gatchina, St. Petersburg 188300, Russia cSt. Petersburg State University, Universitetskaya nab., St. Petersburg 199034, Russia Abstract As was shown recently, non-Abelian vortex strings supported in four- dimensional = 2 supersymmetric QCD with the U(2) gauge group and N Nf = 4 quark multiplets (flavors) become critical superstrings. In addition to the translational moduli non-Abelian strings under consideration carry six orientational and size moduli. Together they form a ten-dimensional target space required for a superstring to be critical. The target space of the string sigma model is a product of the flat four-dimensional space and a Calabi-Yau non-compact threefold, namely, the conifold. We study closed string states which emerge in four dimensions (4D) and identify them with hadrons of arXiv:1704.00825v1 [hep-th] 3 Apr 2017 four-dimensional = 2 QCD. One massless state was found previously: it emerges as a masslessN hypermultiplet associated with the deformation of the complex structure of the conifold. In this paper we find a number of massive states. To this end we exploit the approach used in LST, “Little String Theory,” namely equivalence between the critical string on the conifold and non-critical c = 1 string with the Liouville field and a compact scalar at the self-dual radius. The states we find carry “baryonic” charge (its definition differs from standard).