Strings and M-Theory by Stephen Hawking
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An Introduction to Effective Field Theory
An Introduction to Effective Field Theory Thinking Effectively About Hierarchies of Scale c C.P. BURGESS i Preface It is an everyday fact of life that Nature comes to us with a variety of scales: from quarks, nuclei and atoms through planets, stars and galaxies up to the overall Universal large-scale structure. Science progresses because we can understand each of these on its own terms, and need not understand all scales at once. This is possible because of a basic fact of Nature: most of the details of small distance physics are irrelevant for the description of longer-distance phenomena. Our description of Nature’s laws use quantum field theories, which share this property that short distances mostly decouple from larger ones. E↵ective Field Theories (EFTs) are the tools developed over the years to show why it does. These tools have immense practical value: knowing which scales are important and why the rest decouple allows hierarchies of scale to be used to simplify the description of many systems. This book provides an introduction to these tools, and to emphasize their great generality illustrates them using applications from many parts of physics: relativistic and nonrelativistic; few- body and many-body. The book is broadly appropriate for an introductory graduate course, though some topics could be done in an upper-level course for advanced undergraduates. It should interest physicists interested in learning these techniques for practical purposes as well as those who enjoy the beauty of the unified picture of physics that emerges. It is to emphasize this unity that a broad selection of applications is examined, although this also means no one topic is explored in as much depth as it deserves. -
Soft Gravitons and the Flat Space Limit of Anti-Desitter Space
RUNHETC-2016-15, UTTG-18-16 Soft Gravitons and the Flat Space Limit of Anti-deSitter Space Tom Banks Department of Physics and NHETC Rutgers University, Piscataway, NJ 08854 E-mail: [email protected] Willy Fischler Department of Physics and Texas Cosmology Center University of Texas, Austin, TX 78712 E-mail: fi[email protected] Abstract We argue that flat space amplitudes for the process 2 n gravitons at center of mass → energies √s much less than the Planck scale, will coincide approximately with amplitudes calculated from correlators of a boundary CFT for AdS space of radius R LP , only ≫ when n < R/LP . For larger values of n in AdS space, insisting that all the incoming energy enters “the arena”[20] , implies the production of black holes, whereas there is no black hole production in the flat space amplitudes. We also argue, from unitarity, that flat space amplitudes for all n are necessary to reconstruct the complicated singularity arXiv:1611.05906v3 [hep-th] 8 Apr 2017 at zero momentum in the 2 2 amplitude, which can therefore not be reproduced as → the limit of an AdS calculation. Applying similar reasoning to amplitudes for real black hole production in flat space, we argue that unitarity of the flat space S-matrix cannot be assessed or inferred from properties of CFT correlators. 1 Introduction The study of the flat space limit of correlation functions in AdS/CFT was initiated by the work of Polchinski and Susskind[20] and continued in a host of other papers. Most of those papers agree with the contention, that the limit of Witten diagrams for CFT correlators smeared with appropriate test functions, for operators carrying vanishing angular momentum on the compact 1 space,1 converge to flat space S-matrix elements between states in Fock space. -
Collective Coordinates for D-Branes 1 Introduction
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server UTTG-01-96 Collective Co ordinates for D-branes Willy Fischler, Sonia Paban and Moshe Rozali Theory Group, Department of Physics University of Texas, Austin, Texas 78712 Abstract We develop a formalism for the scattering o D-branes that includes collective co- ordinates. This allows a systematic expansion in the string coupling constant for such pro cesses, including a worldsheet calculation for the D-brane's mass. 1 Intro duction In the recent developments of string theory, solitons play a central role. For example, in the case of duality among various string theories, solitons of a weakly coupled string theory b ecome elementary excitations of the dual theory [1]. Another example, among many others, is the role of solitons in resolving singularities in compacti ed geometries, as they b ecome light[2]. In order to gain more insight in the various asp ects of these recent developments, it is imp ortant to understand the dynamics of solitons in the context of string theory.In this quest one of the to ols at our disp osal is the use of scattering involving these solitons. This includes the scattering of elementary string states o these solitons as well as the scattering among solitons. An imp ortant class of solitons that have emerged are D-branes [4]. In an in uential pap er [3]itwas shown that these D-branes carry R R charges, and are therefore a central ingredient in the aforementioned dualities. -
King's Research Portal
King’s Research Portal DOI: 10.1088/1742-6596/631/1/012089 Document Version Publisher's PDF, also known as Version of record Link to publication record in King's Research Portal Citation for published version (APA): Sarkar, S. (2015). String theory backgrounds with torsion in the presence of fermions and implications for leptogenesis. Journal of Physics: Conference Series, 631(1), [012089]. 10.1088/1742-6596/631/1/012089 Citing this paper Please note that where the full-text provided on King's Research Portal is the Author Accepted Manuscript or Post-Print version this may differ from the final Published version. If citing, it is advised that you check and use the publisher's definitive version for pagination, volume/issue, and date of publication details. And where the final published version is provided on the Research Portal, if citing you are again advised to check the publisher's website for any subsequent corrections. General rights Copyright and moral rights for the publications made accessible in the Research Portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights. •Users may download and print one copy of any publication from the Research Portal for the purpose of private study or research. •You may not further distribute the material or use it for any profit-making activity or commercial gain •You may freely distribute the URL identifying the publication in the Research Portal Take down policy If you believe that this document breaches copyright please contact [email protected] providing details, and we will remove access to the work immediately and investigate your claim. -
Collective Coordinates for D-Branes
UTTG-01-96 Collective Coordinates for D-branes Willy Fischler, Sonia Paban and Moshe Rozali∗ Theory Group, Department of Physics University of Texas, Austin, Texas 78712 Abstract We develop a formalism for the scattering off D-branes that includes collective co- ordinates. This allows a systematic expansion in the string coupling constant for such processes, including a worldsheet calculation for the D-brane’s mass. 1 Introduction In the recent developments of string theory, solitons play a central role. For example, in the case of duality among various string theories, solitons of a weakly coupled string theory become elementary excitations of the dual theory [1]. Another example, among many others, is the role of solitons in resolving singularities in compactified geometries, as they become light [2]. In order to gain more insight in the various aspects of these recent developments, it is important to understand the dynamics of solitons in the context of string theory. In this quest one of the tools at our disposal is the use of scattering involving these solitons. This includes the scattering of elementary string states off these solitons as well as the arXiv:hep-th/9604014v2 11 Apr 1996 scattering among solitons. An important class of solitons that have emerged are D-branes [4]. In an influential paper [3] it was shown that these D-branes carry R R charges, − and are therefore a central ingredient in the aforementioned dualities. These objects are described by simple conformal field theories, which makes them particularly suited for explicit calculations. In this paper we use some of the preliminary ideas about collective coordinates de- veloped in a previous paper [5], to describe the scattering of elementary string states off D-branes. -
Copyright by Juan Felipe Pedraza Avella 2015
Copyright by Juan Felipe Pedraza Avella 2015 The Dissertation Committee for Juan Felipe Pedraza Avella certifies that this is the approved version of the following dissertation: Dynamics of asymptotically AdS spaces and holography Committee: Willy Fischler, Supervisor Jacques Distler Can Kilic Andrew Neitzke Sonia Paban Dynamics of asymptotically AdS spaces and holography by Juan Felipe Pedraza Avella, B.S., M.S. DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN August 2015 Dedicated to my family. Acknowledgments Many people contributed to the research presented in this thesis. I would like to start by thanking my supervisor, prof. Willy Fischler, for his excellent support and guidance over the past five years. I am also grateful to my collaborators: Cesar Ag´on,Tom Banks, Elena C´aceres,Mariano Cherni- coff, Brandon DiNunno, Mohammad Edalati, Bartomeu Fiol, Antonio Garc´ıa, Alberto G¨uijosa,Matthias Ihl, Niko Jokela, Arnab Kundu, Sandipan Kundu, Patricio Letelier,1 Fabio Lora, Phuc Nguyen, Paolo Ospina, Javier Ramos, Walter Tangarife and Di-Lun Yang. For all the time we spent discussing physics, which lead to many successful ideas [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24]. Finally, I would like to thank my fellow students and the professors of the UT Theory Group, for sharing their vast knowledge in individual discussions, seminars and journal club meetings. This material is based upon work supported by the National Science Foundation under Grant PHY-1316033 and by the Texas Cosmology Center, which is supported by the College of Natural Sciences, the Department of As- tronomy at the University of Texas at Austin and the McDonald Observatory. -
The Entropic Force in Reissoner-Nordström-De Sitter
Physics Letters B 797 (2019) 134798 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb The entropic force in Reissoner-Nordström-de Sitter spacetime ∗ Li-Chun Zhang a,b, Ren Zhao a,b, a Institute of Theoretical Physics, Shanxi Datong University, Datong 037009, China b Department of Physics, Shanxi Datong University, Datong 037009, China a r t i c l e i n f o a b s t r a c t Article history: We compare the entropic force between the black hole horizon and the cosmological horizon in Received 2 March 2019 Reissoner-Nordström-de Sitter (RN-dS) spacetime with the Lennard-Jones force between two particles. Received in revised form 21 July 2019 It is found that the former has an extraordinary similarity to the latter. We conclude that the black hole Accepted 22 July 2019 horizon and the cosmological horizon are not pure geometric surface, but have a definite “thickness”, Available online 24 July 2019 which is proportional to the radius of the horizons. In the case of no external force, according to different Editor: M. Cveticˇ initial condition, the relative position of the two horizons will experience first accelerated expansion, then decelerated expansion, or first accelerated contraction, then decelerated contraction. Therefore the whole Universe is oscillating. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction nuity is of the first order; and the one with continuous entropy is of the second order. -
De Sitter Black Holes, Schottky Peaks, and Continuous Heat Engines
arXiv:1907.05883 de Sitter Black Holes, Schottky Peaks and Continuous Heat Engines Clifford V. Johnson Department of Physics and Astronomy University of Southern California Los Angeles, CA 90089-0484, U.S.A. johnson1 [at] usc [dot] edu Abstract Recent work has uncovered Schottky{like peaks in the temperature dependence of key specific heats of certain black hole thermodynamic systems. They signal a finite window of available energy states for the underlying microscopic degrees of freedom. This paper reports on new families of peaks, found for the Kerr and Reissner–Nordstr¨omblack holes in a spacetime with positive cosmological constant. It is known that a system with a highest energy, when coupled arXiv:1907.05883v3 [hep-th] 2 Aug 2019 to two distinct heat baths, can naturally generate a thermodynamic instability, population inversion, a channel for work output. It is noted that these features are all present for de Sitter black holes. It is shown that there are trajectories in parameter space where they behave as generalized masers, operating as continuous heat engines, doing work by shedding angular momentum. It is suggested that bounds on efficiency due to the second law of thermodynamics for general de Sitter black hole solutions could provide powerful consistency checks. 1 Introduction An examination of the behaviour of certain thermodynamic quantities can provide a wealth of useful information about the underlying microscopic quantum mechanical degrees of freedom, sometimes providing key clues as to the formulation of the underlying model. This has a long history, start- ing with early models of gases provided by Einstein [1] (refined by Debye [2]), that derive the temperature dependence of the specific heat at constant volume, CV (T ) starting from simple sta- tistical mechanical considerations of the basic degrees of freedom (for a review see e.g., refs. -
Durham Research Online
Durham Research Online Deposited in DRO: 27 September 2016 Version of attached le: Published Version Peer-review status of attached le: Peer-reviewed Citation for published item: Appels, Michael and Gregory, Ruth and Kubiz§n¡ak,David (2016) 'Thermodynamics of accelerating black holes.', Physical review letters., 117 (13). p. 131303. Further information on publisher's website: http://dx.doi.org/10.1103/PhysRevLett.117.131303 Publisher's copyright statement: This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Additional information: Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full DRO policy for further details. Durham University Library, Stockton Road, Durham DH1 3LY, United Kingdom Tel : +44 (0)191 334 3042 | Fax : +44 (0)191 334 2971 https://dro.dur.ac.uk week ending PRL 117, 131303 (2016) PHYSICAL REVIEW LETTERS 23 SEPTEMBER 2016 Thermodynamics of Accelerating Black Holes † ‡ Michael Appels,1,* Ruth Gregory,1,2, and David Kubizňák2, 1Centre for Particle Theory, Durham University, South Road, Durham DH1 3LE, United Kingdom 2Perimeter Institute, 31 Caroline Street, Waterloo, Ontario N2L 2Y5, Canada (Received 6 May 2016; published 21 September 2016) We address a long-standing problem of describing the thermodynamics of an accelerating black hole. -
Jhep11(2018)072
Published for SISSA by Springer Received: September 12, 2018 Accepted: November 5, 2018 Published: November 12, 2018 Chaos and entanglement spreading in a non-commutative gauge theory JHEP11(2018)072 Willy Fischler,a Viktor Jahnkeb and Juan F. Pedrazac aTheory Group, Department of Physics and Texas Cosmology Center, The University of Texas at Austin, Austin, TX 78712, U.S.A. bDepartamento de F´ısica de Altas Energias, Instituto de Ciencias Nucleares, Universidad Nacional Aut´onomade M´exico, Apartado Postal 70-543, CDMX 04510, M´exico cInstitute for Theoretical Physics, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands E-mail: [email protected], [email protected], [email protected] Abstract: Holographic theories with classical gravity duals are maximally chaotic: they saturate a set of bounds on the spread of quantum information. In this paper we question whether non-locality can affect such bounds. Specifically, we consider the gravity dual of a prototypical theory with non-local interactions, namely, N = 4 non-commutative super Yang Mills. We construct shock waves geometries that correspond to perturbations of the thermofield double state with definite momentum and study several chaos related properties of the theory, including the butterfly velocity, the entanglement velocity, the scrambling time and the maximal Lyapunov exponent. The latter two are unaffected by the non- commutative parameter θ, however, both the butterfly and entanglement velocities increase with the strength of the non-commutativity. This implies that non-local interactions can enhance the effective light-cone for the transfer of quantum information, eluding previously conjectured bounds encountered in the context of local quantum field theory. -
Nonperturbative Formulations of Superstring Theory
NONPERTURBATIVE FORMULATIONS OF SUPERSTRING THEORY BY LUBOSˇ MOTL A dissertation submitted to the Graduate School—New Brunswick Rutgers, The State University of New Jersey in partial fulfillment of the requirements for the degree of Doctor of Philosophy Graduate Program in Physics and Astronomy Written under the direction of Thomas Banks and approved by arXiv:hep-th/0109149v1 19 Sep 2001 New Brunswick, New Jersey October, 2001 ABSTRACT OF THE DISSERTATION Nonperturbative Formulations of Superstring Theory by LuboˇsMotl Dissertation Director: Thomas Banks After a short introduction to Matrix theory, we explain how can one generalize matrix models to describe toroidal compactifications of M-theory and the heterotic vacua with 16 supercharges. This allows us, for the first time in history, to derive the conventional perturbative type IIA string theory known in the 80s within a complete and consistent non- perturbative framework, using the language of orbifold conformal field theory and conformal perturbation methods. A separate chapter is dedicated to the vacua with Hoˇrava-Witten domain walls that carry E8 gauge supermultiplets. Those reduce the gauge symmetry of the matrix model from U(N) to O(N). We also explain why these models contain open membranes. The compactification of M-theory on T 4 involves the so-called (2, 0) supercon- formal field theory in six dimensions, compactified on T 5. A separate chapter describes an interesting topological contribution to the low energy equations of motion on the Coulomb branch of the (2, 0) theory that admits a skyrmionic solution that we call “knitting five- branes”. Then we return to the orbifolds of Matrix theory and construct a formal classical matrix model of the Scherk-Schwarz compactification of M-theory and type IIA string theory as well as type 0 theories. -
What Is String Theory?
hep-th/yymmnn SCIPP-2010/04 What is String Theory? Tom Banks and Michael Dine Santa Cruz Institute for Particle Physics and Department of Physics, University of California, Santa Cruz CA 95064 Abstract We describe, for a general audience, the current state of string theory. We explain that nature is almost certainly not described by string theory as we know it, but that string theory does show us that quantum mechanics and gravity can coexist, and points to the possible theory of quantum gravity which describes the world around us. Directions for research, both on the nature of this theory and its predictions, are described. 1 Introduction Over the past three decades, high energy physicists have developed an exquisite understanding of the laws of nature, governing phenomena down to distances scales as small as 10-17 cm. This Standard Model has proven so successful as to be, at some level, a source of frustration. There are many questions that we would like to understand, for which the Standard Model does not provide satisfying explanations. Some of these - what is the origin of the mass of the electron, quarks, and other particles, why is gravity so much weaker than the other forces, what is the nature of the dark matter - may be answered at the Large Hadron Collider, which, after some setbacks, is beginning operation in Geneva, Switzerland. Others require new theoretical structures. Perhaps the 1.Introduction. Over the past three decades, high energy physicists have developed an exquisite understanding of the laws of nature, governing phenomena down to distances scales as small as 10-17 cm.