DOCSLIB.ORG

Download Enumerative Geometry and String Theory Free Ebook

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Download Enumerative Geometry and String Theory Free Ebook ENUMERATIVE GEOMETRY AND STRING THEORY DOWNLOAD FREE BOOK Sheldon Katz | 206 pages | 31 May 2006 | American Mathematical Society | 9780821836873 | English | Providence, United States Enumerative Geometry and String Theory Chapter 2. The most accessible portal into very exciting recent material. Topological field theory, primitive forms and related topics : — Nuclear Physics B. Bibcode : PThPh. Bibcode : hep. As an example, consider the torus described above. Enumerative Geometry and String Theory standard analogy for this is to consider a multidimensional object such as a garden hose. An example is the red circle in the figure. This problem was solved by the nineteenth-century German mathematician Hermann Schubertwho found that there are Enumerative Geometry and String Theory 2, such lines. Once these topics are in place, the connection between physics and enumerative geometry is made with the introduction of topological quantum field theory and quantum cohomology. Enumerative Geometry and String Theory mirror symmetry relationship is a particular example of what physicists call a duality. Print Price 1: The book contains a lot of extra material that was not included Enumerative Geometry and String Theory the original fifteen lectures. Increasing the dimension from two to four real dimensions, the Calabi—Yau becomes a K3 surface. This problem asks for the number and construction of circles that are tangent to three given circles, points or lines. Topological Quantum Field Theory. Online Price 1: Online ISBN There are infinitely many circles like it on a torus; in fact, the entire surface is a union of such circles. For other uses, see Mirror symmetry. As an example, count the conic sections tangent to five given lines in the projective plane. Greene, Brian InEdward Witten introduced topological string theory, [15] a simplified version of string theory, and physicists showed that there is a version of mirror symmetry for topological string theory. For more information, see Yau and Nadisp. Mirror symmetry was originally discovered by physicists. Advanced search. Mathematicians became interested in this relationship around when Philip CandelasXenia de la OssaPaul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometrya branch of mathematics concerned with counting the number of solutions to geometric questions. Enumerative Geometry in the Projective Plane. Mirror symmetry is also a fundamental tool for doing calculations in string theory, and it has been used to Enumerative Geometry and String Theory aspects of quantum field theorythe formalism that physicists use to describe elementary particles. Halmos - Lester R. See also: Intersection theory. Stable Maps and Enumerative Geometry Nuclear Physics B. Perhaps the most famous example of how ideas from modern physics have revolutionized mathematics is the way string theory has led to an overhaul of enumerative geometry, an area of mathematics that started in the eighteen hundreds. Namespaces Article Talk. In response to these problems, algebraic geometers introduced vague "fudge factors", which were only rigorously justified decades later. Zaslow, Eric Stable Maps and Enumerative Geometry. Quantum Cohomology and Enumerative. Mathematicians became interested in mirror symmetry around when physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that mirror symmetry could be used to solve problems in enumerative geometry [25] that had resisted solution for decades or more. Cover Type: Softcover. The arrays corresponding to mirror Calabi—Yau manifolds are different in general, reflecting the different shapes of the manifolds, but they are related by a certain symmetry. Enumerative Geometry and String Theory, Alexander However, as one approaches the hose, one discovers that it contains a second dimension, its circumference. Enumerative geometry saw spectacular development towards the end of the nineteenth century, at the hands of Hermann Schubert. MAA Book? Chapter 5. These calculations are then used to determine the probabilities of various physical processes in string theory. Mirror symmetry (string theory) For example, mathematicians still lack an understanding of how to construct examples of mirror Calabi—Yau pairs though there has been progress in understanding this issue. One of the earliest problems of enumerative geometry was posed around the year BCE by the ancient Greek mathematician Apolloniuswho asked how many circles in the plane are tangent to three given circles. Chapter 10 — on mechanics classical and quantum — should be called a crash course since it races through a treatment of mechanics based on the Enumerative Geometry and String Theory principle in about ten pages. Mathematicians became interested in mirror symmetry around when physicists Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that mirror symmetry could be used Enumerative Geometry and String Theory solve problems in enumerative geometry Enumerative Geometry and String Theory that had resisted solution for decades or more. Thus, in the language of modern physics, one says that spacetime is four-dimensional. Chapter 5. One of the goals of current research in string theory is to develop models in which the strings represent particles observed in high energy physics experiments. A First Course in String Theory. Along the way, there are some crash courses on intermediate topics which are essential tools for the student of modern mathematics, such as cohomology and other topics in geometry. Random House. For more information, see Yau and Nadisp. In the late s, Lance DixonWolfgang Lerche, Cumrun Vafaand Nick Warner noticed that given such a compactification of string theory, it is not possible to reconstruct uniquely a corresponding Calabi—Yau manifold. Main article: Homological mirror symmetry. September Learn how and when to remove this template message. Wald, Robert Primary MSC: Online ISBN The Calabi—Yau manifolds of primary interest in string theory have six dimensions. Mirror symmetry Monstrous moonshine. So, how many rational curves of degree d are there on a quintic threefold? Enumerative Geometry and String Theory History of string theory First superstring revolution Second superstring revolution String theory landscape. AMS Homepage. For such theories, mirror symmetry is a useful computational tool. Asian Journal of Mathematics. The arrays corresponding to mirror Calabi—Yau manifolds are different in general, reflecting the different shapes of the manifolds, but they are related by a certain symmetry. The derived category of coherent sheaves is constructed using tools from complex geometrya branch of mathematics that describes geometric curves in algebraic Enumerative Geometry and String Theory and solves geometric problems using algebraic equations. Main article: Calabi—Yau manifold. Author s Product display : Sheldon Katz. Many of the important mathematical applications of mirror symmetry belong to the branch of mathematics called enumerative geometry. These strings look like small segments or loops Enumerative Geometry and String Theory ordinary string. The author notes that the book is not self-contained. In enumerative geometry, one is interested in counting the number of solutions to geometric questions, typically using the techniques of algebraic geometry. From there, the goal becomes explaining the more advanced elements of enumerative algebraic geometry. A standard analogy for this is to consider a multidimensional object such as a garden hose. Enumerative geometry This is because a double line intersects every line in the plane, since lines in the projective plane intersect, with multiplicity two because it is doubled, and thus satisfies the same intersection condition intersection of multiplicity two as a nondegenerate conic that is tangent to the line. Readership: Undergraduate and graduate students interested in algebraic geometry or in mathematical physics. Stable Maps and Enumerative Geometry In the B-model, the calculations can be reduced to classical integrals and are much easier. By outsourcing calculations to different theories in this way, theorists can calculate quantities that are impossible to calculate without the use of dualities. Enumerative Geometry and String Theory. But the relevant quadrics here are not in general position. Cellular Decompositions and Line Bundles InEdward Witten introduced topological string theory, [15] a simplified version of string theory, and physicists showed that there is a version of mirror symmetry for topological string theory. Mirror symmetry can be combined with Enumerative Geometry and String Theory dualities to translate calculations in one theory into equivalent calculations in a different theory. Mirror symmetry is also a fundamental tool for doing calculations in string theory, and it has been used to understand aspects of quantum field theorythe formalism that physicists use to describe elementary particles. Mirror symmetry was originally discovered by physicists. Splitting and recombination of strings correspond to particle emission and absorption, giving rise to the interactions between particles. In physics, mirror symmetry is justified on physical grounds. These strings look like small segments or loops of ordinary string. T-duality can be extended from circles to the two-dimensional tori appearing in the decomposition of a K3 surface or to the three-dimensional tori appearing in the decomposition of a six-dimensional Calabi—Yau manifold. It can give
Load more

Recommended publications
  • Relative Mirror Symmetry and Ramifications of a Formula for Gromov-Witten Invariants
    Relative Mirror Symmetry and Ramifications of a Formula for Gromov-Witten Invariants Thesis by Michel van Garrel In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2013 (Defended May 21, 2013) ii c 2013 Michel van Garrel All Rights Reserved iii To my parents Curt and Danielle, the source of all virtues that I possess. To my brothers Cl´ement and Philippe, my best and most fun friends. iv Acknowledgements My greatest thanks go to my advisor Professor Tom Graber, whose insights into the workings of algebraic geometry keep astonishing me and whose ideas were of enormous benefit to me during the pursuit of my Ph.D. My special thanks are given to Professor Yongbin Ruan, who initiated the project on relative mirror symmetry and to whom I am grateful many enjoyable discussions. I am grateful that I am able to count on the continuing support of Professor Eva Bayer and Professor James Lewis. Over the past few years I learned a lot from Daniel Pomerleano, who, among others, introduced me to homological mirror symmetry. Mathieu Florence has been a figure of inspiration and motivation ever since he casually introduced me to algebraic geometry. Finally, my thanks go to the innumerable enjoyable math conversations with Roland Abuaf, Dori Bejleri, Adam Ericksen, Anton Geraschenko, Daniel Halpern-Leistner, Hadi Hedayatzadeh, Cl´ement Hongler, Brian Hwang, Khoa Nguyen, Rom Rains, Mark Shoemaker, Zhiyu Tian, Nahid Walji, Tony Wong and Gjergji Zaimi. v Abstract For a toric Del Pezzo surface S, a new instance of mirror symmetry, said relative, is introduced and developed.
    [Show full text]
  • Stringy T3-Fibrations, T-Folds and Mirror Symmetry
    Stringy T 3-fibrations, T-folds and Mirror Symmetry Ismail Achmed-Zade Arnold-Sommerfeld-Center Work to appear with D. L¨ust,S. Massai, M.J.D. Hamilton March 13th, 2017 Ismail Achmed-Zade (ASC) Stringy T 3-fibrations and applications March 13th, 2017 1 / 24 Overview 1 String compactifications and dualities T-duality Mirror Symmetry 2 T-folds The case T 2 The case T 3 3 Stringy T 3-bundles The useful T 4 4 Conclusion Recap Open Problems Ismail Achmed-Zade (ASC) Stringy T 3-fibrations and applications March 13th, 2017 2 / 24 Introduction Target space Super string theory lives on a 10-dimensional pseudo-Riemannian manifold, e.g. 4 6 M = R × T with metric η G = µν GT 6 In general we have M = Σµν × X , with Σµν a solution to Einsteins equation. M is a solution to the supergravity equations of motion. Non-geometric backgrounds X need not be a manifold. Exotic backgrounds can lead to non-commutative and non-associative gravity. Ismail Achmed-Zade (ASC) Stringy T 3-fibrations and applications March 13th, 2017 3 / 24 T-duality Example Somtimes different backgrounds yield the same physics IIA IIB 9 1 2 2 ! 9 1 1 2 R × S ; R dt R × S ; R2 dt More generally T-duality for torus compactifications is an O(D; D; Z)-transformation (T D ; G; B; Φ) ! (T^D ; G^; B^; Φ)^ Ismail Achmed-Zade (ASC) Stringy T 3-fibrations and applications March 13th, 2017 4 / 24 Mirror Symmetry Hodge diamond of three-fold X and its mirror X^ 1 1 0 0 0 0 0 h1;1 0 0 h1;2 0 1 h1;2 h1;2 1 ! 1 h1;1 h1;1 1 0 h1;1 0 0 h1;2 0 0 0 0 0 1 1 Mirror Symmetry This operation induces the following symmetry IIA IIB ! X ; g X^; g^ Ismail Achmed-Zade (ASC) Stringy T 3-fibrations and applications March 13th, 2017 5 / 24 Mirror Symmetry is T-duality!? SYZ-conjecture [Strominger, Yau, Zaslow, '96] Consider singular bundles T 3 −! X T^3 −! X^ ! ? ? S3 S3 Apply T-duality along the smooth fibers.
    [Show full text]
  • 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.
    [Show full text]
  • VITA Sheldon Katz Urbana, IL 61801 Phone
    VITA Sheldon Katz Urbana, IL 61801 Phone: (217) 265-6258 Education S.B. 1976 Massachusetts Institute of Technology (Mathematics) Ph.D. 1980 Princeton University (Mathematics) Professional Experience University of Illinois Professor 2001{ Dean's Special Advisor, College of LAS 2018{ Interim Chair, Department of Mathematics Fall 2017 Chair, Department of Mathematics 2006{2011 Oklahoma State University Regents Professor 1999{2002 Southwestern Bell Professor 1997{1999 Professor 1994{2002 Associate Professor 1989{1994 Assistant Professor 1987{1989 University of Oklahoma Assistant Professor (tenure 1987) 1984{1987 University of Utah Instructor 1980{1984 Visiting Positions MSRI Simons Visiting Professor 2018 Simons Center 2012 Mittag-Leffler Institute, Sweden Visiting Professor 1997 Duke University Visiting Professor 1991{1992 University of Bayreuth, West Germany Visiting Professor 1989 Institute for Advanced Study Member 1982{1983 Publications 1. Degenerations of quintic threefolds and their lines. Duke Math. Jour. 50 (1983), 1127{1135. 2. Lines on complete intersection threefolds with K=0. Math. Z. 191 (1986), 297{302. 3. Tangents to a multiple plane curve. Pac. Jour. Math. 124 (1986), 321{331. 4. On the finiteness of rational curves on quintic threefolds. Comp. Math. 60 (1986), 151{162. 5. Hodge numbers of linked surfaces in P4. Duke Math. Jour. 55 (1987), 89{95. 6. The cubo-cubic transformation of P3 is very special. Math. Z. 195 (1987), 255{257. 7. Iteration of Multiple point formulas and applications to conics. Proceed- ings of the Algebraic Geometry Conference, Sundance, UT 1986, SLN 1311, 147{155. 8. Varieties cut out by quadrics: Scheme theoretic versus homogeneous gen- eration of ideals (with L.
    [Show full text]
  • Mirror Symmetry Is a Phenomenon Arising in String Theory in Which Two Very Different Manifolds Give Rise to Equivalent Physics
    Clay Mathematics Monographs 1 Volume 1 Mirror symmetry is a phenomenon arising in string theory in which two very different manifolds give rise to equivalent physics. Such a correspondence has Mirror Symmetry Mirror significant mathematical consequences, the most familiar of which involves the enumeration of holomorphic curves inside complex manifolds by solving differ- ential equations obtained from a “mirror” geometry. The inclusion of D-brane states in the equivalence has led to further conjectures involving calibrated submanifolds of the mirror pairs and new (conjectural) invariants of complex manifolds: the Gopakumar Vafa invariants. This book aims to give a single, cohesive treatment of mirror symmetry from both the mathematical and physical viewpoint. Parts 1 and 2 develop the neces- sary mathematical and physical background “from scratch,” and are intended for readers trying to learn across disciplines. The treatment is focussed, developing only the material most necessary for the task. In Parts 3 and 4 the physical and mathematical proofs of mirror symmetry are given. From the physics side, this means demonstrating that two different physical theories give isomorphic physics. Each physical theory can be described geometrically, and thus mirror symmetry gives rise to a “pairing” of geometries. The proof involves applying R ↔ 1/R circle duality to the phases of the fields in the gauged linear sigma model. The mathematics proof develops Gromov-Witten theory in the algebraic MIRROR SYMMETRY setting, beginning with the moduli spaces of curves and maps, and uses localiza- tion techniques to show that certain hypergeometric functions encode the Gromov-Witten invariants in genus zero, as is predicted by mirror symmetry.
    [Show full text]
  • A Survey of Calabi-Yau Manifolds
    Surveys in Differential Geometry XIII A survey of Calabi-Yau manifolds Shing-Tung Yau Contents 1. Introduction 278 2. General constructions of complete Ricci-flat metrics in K¨ahler geometry 278 2.1. The Ricci tensor of Calabi-Yau manifolds 278 2.2. The Calabi conjecture 279 2.3. Yau’s theorem 279 2.4. Calabi-Yau manifolds and Calabi-Yau metrics 280 2.5. Examples of compact Calabi-Yau manifolds 281 2.6. Noncompact Calabi-Yau manifolds 282 2.7. Calabi-Yau cones: Sasaki-Einstein manifolds 283 2.8. The balanced condition on Calabi-Yau metrics 284 3. Moduli and arithmetic of Calabi-Yau manifolds 285 3.1. Moduli of K3 surfaces 285 3.2. Moduli of high dimensional Calabi-Yau manifolds 286 3.3. The modularity of Calabi–Yau threefolds over Q 287 4. Calabi-Yau manifolds in physics 288 4.1. Calabi-Yau manifolds in string theory 288 4.2. Calabi-Yau manifolds and mirror symmetry 289 4.3. Mathematics inspired by mirror symmetry 291 5. Invariants of Calabi-Yau manifolds 291 5.1. Gromov-Witten invariants 291 5.2. Counting formulas 292 5.3. Proofs of counting formulas for Calabi-Yau threefolds 293 5.4. Integrability of mirror map and arithmetic applications 293 5.5. Donaldson-Thomas invariants 294 5.6. Stable bundles and sheaves 296 5.7. Yau-Zaslow formula for K3 surfaces 296 5.8. Chern-Simons knot invariants, open strings and string dualities 297 c 2009 International Press 277 278 S.-T. YAU 6. Homological mirror symmetry 299 7. SYZ geometric interpretation of mirror symmetry 300 7.1.
    [Show full text]
  • Perspectives on Geometric Analysis
    Surveys in Differential Geometry X Perspectives on geometric analysis Shing-Tung Yau This essay grew from a talk I gave on the occasion of the seventieth anniversary of the Chinese Mathematical Society. I dedicate the lecture to the memory of my teacher S.S. Chern who had passed away half a year before (December 2004). During my graduate studies, I was rather free in picking research topics. I[731] worked on fundamental groups of manifolds with non-positive curva- ture. But in the second year of my studies, I started to look into differential equations on manifolds. However, at that time, Chern was very much inter- ested in the work of Bott on holomorphic vector fields. Also he told me that I should work on Riemann hypothesis. (Weil had told him that it was time for the hypothesis to be settled.) While Chern did not express his opinions about my research on geometric analysis, he started to appreciate it a few years later. In fact, after Chern gave a course on Calabi’s works on affine geometry in 1972 at Berkeley, S.Y. Cheng told me about these inspiring lec- tures. By 1973, Cheng and I started to work on some problems mentioned in Chern’s lectures. We did not realize that the great geometers Pogorelov, Calabi and Nirenberg were also working on them. We were excited that we solved some of the conjectures of Calabi on improper affine spheres. But soon after we found out that Pogorelov [563] published his results right be- fore us by different arguments. Nevertheless our ideas are useful in handling other problems in affine geometry, and my knowledge about Monge-Amp`ere equations started to broaden in these years.
    [Show full text]
  • Syz Mirror Symmetry for Toric Varieties
    SYZ MIRROR SYMMETRY FOR TORIC VARIETIES KWOKWAI CHAN Abstract. We survey recent developments in the study of SYZ mirror sym- metry for compact toric and toric Calabi-Yau varieties, with a special emphasis on works of the author and his collaborators. Contents 1. The SYZ proposal 1 1.1. Semi-flat SYZ: a toy example 2 2. A quick review on toric varieties 5 3. Mirror symmetry for compact toric varieties 6 3.1. Landau-Ginzburg models as mirrors 6 3.2. The SYZ construction 7 3.3. Open mirror theorems 11 4. Mirror symmetry for toric Calabi-Yau varieties 15 4.1. Physicists' mirrors 15 4.2. The SYZ construction 17 4.3. Period integrals and disk counting { a conjecture of Gross-Siebert 21 Acknowledgment 23 References 23 1. The SYZ proposal In 1996, drawing on the new idea of D-branes from string theory, Strominger, Yau and Zaslow [76] made a ground-breaking proposal to explain mirror symmetry geometrically as a Fourier{type transform, known as T-duality. Conjecture 1.1 (The SYZ conjecture [76]). If X and Xˇ are Calabi-Yau manifolds mirror to each other, then (i) both X and Xˇ admit special Lagrangian torus fibrations with sections ρ : X ! B and ρˇ : Xˇ ! B over the same base which are fiberwise dual to each other in the sense that regular fibers ρ−1(b) ⊂ X and ρˇ−1(b) ⊂ Xˇ over the same point b 2 B are dual tori, and (ii) there exist Fourier{type transforms which exchange symplectic-geometric (resp. complex-geometric) data on X with complex-geometric (resp.
    [Show full text]
  • String-Math 2012
    Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors Volume 90 String-Math 2012 July 16–21, 2012 Universitat¨ Bonn, Bonn, Germany Ron Donagi Sheldon Katz Albrecht Klemm David R. Morrison Editors 2010 Mathematics Subject Classification. Primary 11G55, 14D21, 14F05, 14J28, 14M30, 32G15, 53D18, 57M27, 81T40. 83E30. Library of Congress Cataloging-in-Publication Data String-Math (Conference) (2012 : Bonn, Germany) String-Math 2012 : July 16-21, 2012, Universit¨at Bonn, Bonn, Germany/Ron Donagi, Sheldon Katz, Albrecht Klemm, David R. Morrison, editors. pages cm. – (Proceedings of symposia in pure mathematics; volume 90) Includes bibliographical references. ISBN 978-0-8218-9495-8 (alk. paper) 1. Geometry, Algebraic–Congresses. 2. Quantum theory– Mathematics–Congresses. I. Donagi, Ron, editor. II. Katz, Sheldon, 1956- editor. III. Klemm, Albrecht, 1960- editor. IV. Morrison, David R., 1955- editor. V. Title. QA564.S77 2012 516.35–dc23 2015017523 DOI: http://dx.doi.org/10.1090/pspum/090 Color graphic policy. Any graphics created in color will be rendered in grayscale for the printed version unless color printing is authorized by the Publisher. In general, color graphics will appear in color in the online version. Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy select pages for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given.
    [Show full text]
  • Annual Report 2010 Report Annual IPMU ANNUAL REPORT 2010 April 2010 April – March 2011March
    IPMU April 2010–March 2011 Annual Report 2010 IPMU ANNUAL REPORT 2010 April 2010 – March 2011 World Premier International Institute for the Physics and Mathematics of the Universe (IPMU) Research Center Initiative Todai Institutes for Advanced Study Todai Institutes for Advanced Study The University of Tokyo 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan TEL: +81-4-7136-4940 FAX: +81-4-7136-4941 http://www.ipmu.jp/ History (April 2010–March 2011) April • Workshop “Recent advances in mathematics at IPMU II” • Press Release “Shape of dark matter distribution” • Mini-Workshop “Cosmic Dust” May • Shaw Prize to David Spergel • Press Release “Discovery of the most distant cluster of galaxies” • Press Release “An unusual supernova may be a missing link in stellar evolution” June • CL J2010: From Massive Galaxy Formation to Dark Energy • Press Conference “Study of type Ia supernovae strengthens the case for the dark energy” July • Institut d’Astrophysique de Paris Medal (France) to Ken’ichi Nomoto • IPMU Day of Extra-galactic Astrophysics Seminars: Chemical Evolution August • Workshop “Galaxy and cosmology with Thirty Meter Telescope (TMT)” September • Subaru Future Instrumentation Workshop • Horiba International Conference COSMO/CosPA October • The 3rd Anniversary of IPMU, All Hands Meeting and Reception • Focus Week “String Cosmology” • Nishinomiya-Yukawa Memorial Prize to Eiichiro Komatsu • Workshop “Evolution of massive galaxies and their AGNs with the SDSS-III/BOSS survey” • Open Campus Day: Public lecture, mini-lecture and exhibits November
    [Show full text]
  • Black Hole Entropy, Marginal Stability and Mirror Symmetry
    hep-th/0610044 DUKE-CGTP-06-01 SLAC-PUB-12048 October 2006 Black Hole Entropy, Marginal Stability and Mirror Symmetry Paul S. Aspinwall1, Alexander Maloney2 and Aaron Simons3 1 Center for Geometry and Theoretical Physics, Box 90318 Duke University, Durham, NC 27708-0318 2 School of Natural Sciences, Institute for Advanced Study Einstein Dr., Princeton, NJ 08540 3 Department of Physics, Harvard University, Cambridge, MA 02138 Abstract We consider the superconformal quantum mechanics associated to BPS black holes in type IIB Calabi–Yau compactifications. This quantum mechanics describes the dynamics of D- branes in the near-horizon attractor geometry of the black hole. In many cases, the black hole entropy can be found by counting the number of chiral primaries in this quantum mechanics. Both the attractor mechanism and notions of marginal stability play important roles in generating the large number of microstates required to explain this entropy. We compute the microscopic entropy explicitly in a few different cases, where the theory reduces to quantum mechanics on the moduli space of special Lagrangians. Under certain assumptions, the problem may be solved by implementing mirror symmetry as three T-dualities: this is essentially the mirror of a calculation by Gaiotto, Strominger and Yin. In some simple cases, the calculation may be done in greater generality without resorting to conjectures about mirror symmetry. For example, the K3 T 2 case may be studied precisely using the Fourier-Mukai transform. × email: [email protected], [email protected], [email protected] Submitted to Journal of High Energy Physics (JHEP) Work supported in part by Department of Energy contract DE-AC02-76SF00515 SLAC, Stanford Univesity, Stanford, CA 94309 1 Introduction The study of quantum mechanical black holes continues to provide new insights into the basic structure of string theory and quantum gravity.
    [Show full text]
  • JHEP05(2021)013 Springer -Structure May 3, 2021 : March 29, 2021 : -Structure Met- SU(3)
    Published for SISSA by Springer Received: December 21, 2020 Accepted: March 29, 2021 Published: May 3, 2021 Moduli-dependent Calabi-Yau and SU(3)-structure metrics from machine learning JHEP05(2021)013 Lara B. Anderson,a Mathis Gerdes,b James Gray,a Sven Krippendorf,b Nikhil Raghurama and Fabian Ruehlec,d aDepartment of Physics, Robeson Hall, Virginia Tech, Blacksburg, VA 24061, U.S.A. bArnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, Theresienstr. 37, 80333 Munich, Germany cCERN, Theoretical Physics Department 1, Esplanade des Particules, Geneva 23, CH-1211, Switzerland dRudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, U.K. E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: We use machine learning to approximate Calabi-Yau and SU(3)-structure met- rics, including for the first time complex structure moduli dependence. Our new methods furthermore improve existing numerical approximations in terms of accuracy and speed. Knowing these metrics has numerous applications, ranging from computations of crucial aspects of the effective field theory of string compactifications such as the canonical nor- malizations for Yukawa couplings, and the massive string spectrum which plays a crucial role in swampland conjectures, to mirror symmetry and the SYZ conjecture. In the case of SU(3) structure, our machine learning approach allows us to engineer metrics with certain torsion properties. Our methods are demonstrated for Calabi-Yau and SU(3)-structure manifolds based on a one-parameter family of quintic hypersurfaces in P4.
    [Show full text]