String Theory and M-Theory: a Modern Introduction Katrin Becker, Melanie Becker, and John H
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Stephen Hawking (1942–2018) World-Renowned Physicist Who Defied the Odds
COMMENT OBITUARY Stephen Hawking (1942–2018) World-renowned physicist who defied the odds. hen Stephen Hawking was speech synthesizer processed his words and diagnosed with motor-neuron generated the androidal accent that became disease at the age of 21, it wasn’t his trademark. In this way, he completed his Wclear that he would finish his PhD. Against best-selling book A Brief History of Time all expectations, he lived on for 55 years, (Bantam, 1988), which propelled him to becoming one of the world’s most celebrated celebrity status. IAN BERRY/MAGNUM scientists. Had Hawking achieved equal distinction Hawking, who died on 14 March 2018, was in any other branch of science besides cos- born in Oxford, UK, in 1942 to a medical- mology, it probably would not have had the researcher father and a philosophy-graduate same resonance with a worldwide public. As mother. After attending St Albans School I put it in The Telegraph newspaper in 2007, near London, he earned a first-class degree “the concept of an imprisoned mind roaming in physics from the University of Oxford. He the cosmos” grabbed people’s imagination. began his research career in 1962, enrolling In 1965, Stephen married Jane Wilde. as a graduate student in a group at the Uni- After 25 years of marriage, and three versity of Cambridge led by one of the fathers children, the strain of Stephen’s illness of modern cosmology, Dennis Sciama. and of sharing their home with a team of The general theory of relativity was at that nurses became too much and they sepa- time undergoing a renaissance, initiated in rated, divorcing in 1995. -
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. -
CERN Celebrates Discoveries
INTERNATIONAL JOURNAL OF HIGH-ENERGY PHYSICS CERN COURIER VOLUME 43 NUMBER 10 DECEMBER 2003 CERN celebrates discoveries NEW PARTICLES NETWORKS SPAIN Protons make pentaquarks p5 Measuring the digital divide pl7 Particle physics thrives p30 16 KPH impact 113 KPH impact series VISyN High Voltage Power Supplies When the objective is to measure the almost immeasurable, the VISyN-Series is the detector power supply of choice. These multi-output, card based high voltage power supplies are stable, predictable, and versatile. VISyN is now manufactured by Universal High Voltage, a world leader in high voltage power supplies, whose products are in use in every national laboratory. For worldwide sales and service, contact the VISyN product group at Universal High Voltage. Universal High Voltage Your High Voltage Power Partner 57 Commerce Drive, Brookfield CT 06804 USA « (203) 740-8555 • Fax (203) 740-9555 www.universalhv.com Covering current developments in high- energy physics and related fields worldwide CERN Courier (ISSN 0304-288X) is distributed to member state governments, institutes and laboratories affiliated with CERN, and to their personnel. It is published monthly, except for January and August, in English and French editions. The views expressed are CERN not necessarily those of the CERN management. Editor Christine Sutton CERN, 1211 Geneva 23, Switzerland E-mail: [email protected] Fax:+41 (22) 782 1906 Web: cerncourier.com COURIER Advisory Board R Landua (Chairman), P Sphicas, K Potter, E Lillest0l, C Detraz, H Hoffmann, R Bailey -
String Theory in Magnetic Monopole Backgrounds
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server EFI-98-58, ILL-(TH)-98-06 hep-th/9812027 String Theory in Magnetic Monopole Backgrounds David Kutasov1,FinnLarsen1, and Robert G. Leigh2 1Enrico Fermi Institute, University of Chicago, 5640 S. Ellis Av., Chicago, IL 60637 2Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 We discuss string propagation in the near-horizon geometry generated by Neveu-Schwarz fivebranes, Kaluza-Klein monopoles and fundamental strings. When the fivebranes and KK monopoles are wrapped around a compact four-manifold , the geometry is AdS S3/ZZ and the M 3 × N ×M spacetime dynamics is expected to correspond to a local two dimensional conformal field theory. We determine the moduli space of spacetime CFT’s, study the spectrum of the theory and compare the chiral primary operators obtained in string theory to supergravity expectations. 12/98 1. Introduction It is currently believed that many (perhaps all) vacua of string theory have the prop- erty that their spacetime dynamics can be alternatively described by a theory without gravity [1,2,3,4]. This theory is in general non-local, but in certain special cases it is ex- pected to become a local quantum field theory (QFT). It is surprising that string dynamics can be equivalent to a local QFT. A better understanding of this equivalence would have numerous applications to strongly coupled gauge theory, black hole physics and a non- perturbative formulation of string theory. An important class of examples for which string dynamics is described by local QFT is string propagation on manifolds that include an anti-de-Sitter spacetime AdSp+1[3,5,6]. -
Non-Holomorphic Cycles and Non-BPS Black Branes Arxiv
Non-Holomorphic Cycles and Non-BPS Black Branes Cody Long,1;2 Artan Sheshmani,2;3;4 Cumrun Vafa,1 and Shing-Tung Yau2;5 1Jefferson Physical Laboratory, Harvard University Cambridge, MA 02138, USA 2Center for Mathematical Sciences and Applications, Harvard University Cambridge, MA 02139, USA 3Institut for Matematik, Aarhus Universitet 8000 Aarhus C, Denmark 4 National Research University Higher School of Economics, Russian Federation, Laboratory of Mirror Symmetry, Moscow, Russia, 119048 5Department of Mathematics, Harvard University Cambridge, MA 02138, USA We study extremal non-BPS black holes and strings arising in M-theory compactifica- tions on Calabi-Yau threefolds, obtained by wrapping M2 branes on non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the attractor mechanism we compute the black hole mass and black string tension, leading to a conjectural for- mula for the asymptotic volumes of connected, locally volume-minimizing representa- tives of non-holomorphic, even-dimensional homology classes in the threefold, without arXiv:2104.06420v1 [hep-th] 13 Apr 2021 knowledge of an explicit metric. In the case of divisors we find examples where the vol- ume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and leading to stable, non-BPS strings. We also compute the central charges of non-BPS strings in F-theory via a near-horizon AdS3 limit in 6d which, upon compactification on a circle, account for the asymptotic entropy of extremal non- supersymmetric 5d black holes (i.e., the asymptotic count of non-holomorphic minimal 2-cycles). -
Towards a String Dual of SYK Arxiv:2103.03187V1 [Hep-Th] 4 Mar
Towards A String Dual of SYK Akash Goel and Herman Verlinde Department of Physics, Princeton University, Princeton, NJ 08544, USA Abstract: We propose a paradigm for realizing the SYK model within string theory. Using the large N matrix description of c < 1 string theory, we show that the effective theory on a large number Q of FZZT D-branes in (p; 1) minimal string theory takes the form of the disorder averaged SYK model with J p interaction. The SYK fermions represent open strings between the FZZT branes and the ZZ branes that underly the matrix model. The continuum SYK dynamics arises upon taking the large Q limit. We observe several qualitative and quantitative links between the SYK model and (p; q) minimal string theory and propose that the two describe different phases of a single system. We comment on the dual string interpretation of double scaled SYK and on the relevance of our results to the recent discussion of the role of ensemble averaging in holography. arXiv:2103.03187v2 [hep-th] 24 Aug 2021 Contents 1 Introduction2 2 SYK from the Two Matrix Model4 2.1 FZZT-branes in the two matrix model4 2.2 Kontsevich matrix model from FZZT branes6 2.3 SYK matrix model from FZZT branes7 3 Towards the Continuum SYK model8 3.1 Non-commutative SYK8 4 From Minimal Strings to SYK 10 4.1 SYK and the (p; q) spectral curve 11 4.2 FZZT brane correlation function 12 4.3 Minimal String-SYK phase diagram 13 5 SYK as a Non-Critical String 14 6 Conclusion 16 A D-branes in Minimal String Theory 18 A.1 Matrices and the non-commutative torus 23 A.2 Non-commutative SYK 24 A.3 Matrix SYK 26 A.4 Mapping between Matrix SYK and Non-Commutative SYK 27 { 1 { 1 Introduction The SYK model is the prototype of a maximally chaotic quantum system with low energy dynamics given by near-AdS2 gravity. -
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. -
Supergravity at 40: Reflections and Perspectives(∗)
RIVISTA DEL NUOVO CIMENTO Vol. 40, N. 6 2017 DOI 10.1393/ncr/i2017-10136-6 ∗ Supergravity at 40: Reflections and perspectives( ) S. Ferrara(1)(2)(3)andA. Sagnotti(4) (1) Theoretical Physics Department, CERN CH - 1211 Geneva 23, Switzerland (2) INFN - Laboratori Nazionali di Frascati - Via Enrico Fermi 40 I-00044 Frascati (RM), Italy (3) Department of Physics and Astronomy, Mani L. Bhaumik Institute for Theoretical Physics U.C.L.A., Los Angeles CA 90095-1547, USA (4) Scuola Normale Superiore e INFN - Piazza dei Cavalieri 7, I-56126 Pisa, Italy received 15 February 2017 Dedicated to John H. Schwarz on the occasion of his 75th birthday Summary. — The fortieth anniversary of the original construction of Supergravity provides an opportunity to combine some reminiscences of its early days with an assessment of its impact on the quest for a quantum theory of gravity. 280 1. Introduction 280 2. The early times 282 3. The golden age 283 4. Supergravity and particle physics 284 5. Supergravity and string theory 286 6. Branes and M-theory 287 7. Supergravity and the AdS/CFT correspondence 288 8. Conclusions and perspectives ∗ ( ) Based in part on the talk delivered by S.F. at the “Special Session of the DISCRETE2016 Symposium and the Leopold Infeld Colloquium”, in Warsaw, on December 1 2016, and on a joint CERN Courier article. c Societ`a Italiana di Fisica 279 280 S. FERRARA and A. SAGNOTTI 1. – Introduction The year 2016 marked the fortieth anniversary of the discovery of Supergravity (SGR) [1], an extension of Einstein’s General Relativity [2] (GR) where Supersymme- try, promoted to a gauge symmetry, accompanies general coordinate transformations. -
Black Brane Evaporation Through D-Brane Bubble Nucleation
HIP-2021-20/TH Black brane evaporation through D-brane bubble nucleation Oscar Henriksson∗ Department of Physics and Helsinki Institute of Physics P.O. Box 64, FI-00014 University of Helsinki, Finland Abstract We study the process of black brane evaporation through the emission of D-branes. Gravi- tational solutions describing black branes in asymptotically anti-de Sitter spacetimes, which are holographically dual to field theory states at finite temperature and density, have previously been found to exhibit an instability due to brane nucleation. Working in the setting of D3-branes on the conifold, we construct static Euclidean solutions describing this nucleation to leading order | D3-branes bubbling off the horizon. Furthermore, we analyze the late-time dynamics of such a D3-brane bubble as it expands and find a steady-state solution including the wall profile and its speed. CONTENTS I. Introduction 2 II. Gravity solutions and field theory dual 3 III. The D3-brane effective action 4 IV. Bubble nucleation 6 arXiv:2106.13254v1 [hep-th] 24 Jun 2021 V. Late time expansion 8 VI. Discussion 11 Acknowledgments 12 References 12 ∗ oscar.henriksson@helsinki.fi 1 I. INTRODUCTION Black holes are unstable to evaporation due to Hawking radiation. Though this fact is on firm theoretical footing, there are still many open questions regarding the precise details of this evaporation, some of which may require a complete theory of quantum gravity to settle. String theory is a strong candidate for such a theory. Besides strings, this framework also introduces other extended objects known as branes. These dynamical objects also gravitate, and a large number of them can be described in the supergravity limit of string theory as a black brane. -
Chaos in Matrix Models and Black Hole Evaporation
LLNL-JRNL-681857 UCB-PTH-16/01 SU-ITP-16/02 YITP-16-5 Chaos in Matrix Models and Black Hole Evaporation Evan Berkowitz,a1 Masanori Hanadabcd2 and Jonathan Maltzeb3 a Nuclear and Chemical Sciences Division, Lawrence Livermore National Laboratory, Livermore CA 94550, USA bStanford Institute for Theoretical Physics, Stanford University, Stanford, CA 94305, USA cYukawa Institute for Theoretical Physics, Kyoto University, Kitashirakawa Oiwakecho, Sakyo-ku, Kyoto 606-8502, Japan dThe Hakubi Center for Advanced Research, Kyoto University, Yoshida Ushinomiyacho, Sakyo-ku, Kyoto 606-8501, Japan e Berkeley Center for Theoretical Physics, University of California at Berkeley, Berkeley, CA 94720, USA Abstract Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question |especially aspects of this question such as a black hole's negative specific heat|we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, arXiv:1602.01473v3 [hep-th] 15 Jan 2019 has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. -
What Lattice Theorists Can Do for Superstring/M-Theory
July 26, 2016 0:28 WSPC/INSTRUCTION FILE review˙2016July23 International Journal of Modern Physics A c World Scientific Publishing Company What lattice theorists can do for superstring/M-theory MASANORI HANADA Yukawa Institute for Theoretical Physics Kyoto University, Kyoto 606-8502, JAPAN The Hakubi Center for Advanced Research Kyoto University, Kyoto 606-8501, JAPAN Stanford Institute for Theoretical Physics Stanford University, Stanford, CA 94305, USA [email protected] The gauge/gravity duality provides us with nonperturbative formulation of superstring/M-theory. Although inputs from gauge theory side are crucial for answering many deep questions associated with quantum gravitational aspects of superstring/M- theory, many of the important problems have evaded analytic approaches. For them, lattice gauge theory is the only hope at this moment. In this review I give a list of such problems, putting emphasis on problems within reach in a five-year span, including both Euclidean and real-time simulations. Keywords: Lattice Gauge Theory; Gauge/Gravity Duality; Quantum Gravity. PACS numbers:11.15.Ha,11.25.Tq,11.25.Yb,11.30.Pb Preprint number:YITP-16-28 1. Introduction During the second superstring revolution, string theorists built a beautiful arXiv:1604.05421v2 [hep-lat] 23 Jul 2016 framework for quantum gravity: the gauge/gravity duality.1, 2 It claims that superstring/M-theory is equivalent to certain gauge theories, at least about certain background spacetimes (e.g. black brane background, asymptotically anti de-Sitter (AdS) spacetime). Here the word ‘equivalence’ would be a little bit misleading, be- cause it is not clear how to define string/M-theory nonperturbatively; superstring theory has been formulated based on perturbative expansions, and M-theory3 is defined as the strong coupling limit of type IIA superstring theory, where the non- perturbative effects should play important roles. -
Is String Theory Holographic? 1 Introduction
Holography and large-N Dualities Is String Theory Holographic? Lukas Hahn 1 Introduction1 2 Classical Strings and Black Holes2 3 The Strominger-Vafa Construction3 3.1 AdS/CFT for the D1/D5 System......................3 3.2 The Instanton Moduli Space.........................6 3.3 The Elliptic Genus.............................. 10 1 Introduction The holographic principle [1] is based on the idea that there is a limit on information content of spacetime regions. For a given volume V bounded by an area A, the state of maximal entropy corresponds to the largest black hole that can fit inside V . This entropy bound is specified by the Bekenstein-Hawking entropy A S ≤ S = (1.1) BH 4G and the goings-on in the relevant spacetime region are encoded on "holographic screens". The aim of these notes is to discuss one of the many aspects of the question in the title, namely: "Is this feature of the holographic principle realized in string theory (and if so, how)?". In order to adress this question we start with an heuristic account of how string like objects are related to black holes and how to compare their entropies. This second section is exclusively based on [2] and will lead to a key insight, the need to consider BPS states, which allows for a more precise treatment. The most fully understood example is 1 a bound state of D-branes that appeared in the original article on the topic [3]. The third section is an attempt to review this construction from a point of view that highlights the role of AdS/CFT [4,5].