DOCSLIB.ORG

Compactifying All Spatial Dimensions of the Universe

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Compactifying All Spatial Dimensions of the Universe FACULTY OF SCIENCE Compactifying all spatial dimensions of the universe Quentin Decant Thesis supervisor: Thesis submitted for the degree of prof. dr. Thomas Van Riet Master of Science of Physics, option Research Academic year 2017 – 2018 © Copyright KU Leuven Without written permission of the thesis supervisor and the author it is forbidden to reproduce or adapt in any form or by any means any part of this publication. Requests for obtaining the right to reproduce or utilize parts of this publication should be addressed to Faculteit Wetenschappen, Geel Huis, Kasteelpark Arenberg 11 bus 2100, B-3001 Leuven (Heverlee), +32-16-321401. A written permission of the thesis supervisor is also required to use the meth- ods, products, schematics and programs described in this work for industrial or commercial use, and for submitting this publication in scientific contests. Preface This thesis would not have been what it is now without the direct or indirect help of other people. I use this text to thank them. To start I would like to thank prof. dr. Thomas Van Riet for giving me the opportunity to write a thesis on such an exciting and interesting subject. I learned a lot from you this year, and the fact that you had the patience for allowing me to walk into your office anytime to ask questions was very much appreciated. I would like to express my gratitude to some of my fellow master students: David, Arno, Sam, Kristof, Kesha, for the good times at the office. My special thanks go to Vincent and Rob, with whom I had a lot of interesting and helpful discussion about physics. All the other people at the institute are also thanked, I really felt at home at the institute. The coffee breaks at four o’clock were really fun and a good relaxation moment. I also would like to thank my friends for all the good times we had together, not only this year, but the past five years. You made my student time very fun and memorable. I would like to express my deep gratitude to Anne, not only for the correcting of typos in my thesis. This thesis would simply not have been possible without all your support this past year. To conclude I am the most thankful to my parents. You always made sure that I had everything I needed to succeed. You continued to believe in me no matter what, and the freedom that you gave me due to this trust made me the person who I am now. Quentin Decant i Scientific summary This thesis introduces a new approach towards solving the cosmological constant problem. This is a very subtle issue that plagues the high energy physics community for decades now. The problem is a naturalness problem which we formulated as follows: the enormous difference between the Hubble scale and the length scale of possible extra dimensions, is something very unnatural. These hypothetical extra dimensions are a fundamental concept in modern theoretical physics and are an essential ingredient in superstring theory, the most studied theory of quantum gravity. Understanding the reason that the dimensions we live are so much bigger compared to the extra dimensions is therefore an important and fundamental question. We try to understand this unnatural situation by starting from a more natural situ- ation and evolve via a dynamical mechanism to the unnatural one. More concretely we want to start from a situation were all the spatial dimensions of our universe are treated equally. We take our natural situation to be that all dimensions are compact because we know from observations that the size of the universe has grown in time. To obtain such an initial condition for our universe we try to find one dimensional vacua of string theory, such that the scalar potential obtained from compactification admits only a meta-stable vacuum. This can be obtained by having a scalar potential which has only a local minimum for the volume modulus, no global one. In this case, classically the system will stay in this local minimum. However, quantum mechanically, the volume modulus will tunnel out of this meta-stable state, resulting in a spontaneous decompactification of some of the dimensions. This then gives rise to a universe which has some very large dimensions, and where the others remain compact. Even if there are no extra dimensions this mechanism could maybe provide initial conditions for inflation. The mistake of associating this mechanism to old inflation could easily be made, however they are not the same thing. In old inflation a four dimensional scalar field tunnels out of false vacuum state, we consider a one-dimensional field in a one-dimensional vacuum, which is a different thing. This means that the issues of old inflation do not automatically apply to our model. Under the approximation of smeared orientifold planes we derive that one- dimensional vacua do exist in string theory, and it is very likely that performing the calculation with localised planes results in the same conclusion. A simple compacti- fication of these solutions yields an unfixed modulus, and is therefore not suited as a realisation of our mechanism. We did not investigate this further, but changed our approach. String theory and other theories with extra dimensions need to have phenomeno- logical acceptable vacua, otherwise they can not describe the world we live in. On this fact the following reasoning is based. If we can compactify a four dimensional theory to one dimension, and this new theory admits a meta-stable vacuum, then the decompactification can lead to the theory we started from. Therefore we took four dimensional gravity combined with electromagnetism, axions and a cosmological constant, and investigated if we can compactify this to a theory admitting a one ii SCIENTIFIC SUMMARY dimensional vacuum. This led us to a theorem excluding stable one-dimensional vacua obtained by compactifications using the above mentioned ingredients,. This turned out not to be a bad thing. We found that meta-stable pockets can appear in the scalar potential. Dependent on the quantum corrections in our model, they are classicaly stable and yield compact periodically blowing-up and deflating universes. However these pockets are only local minima, so these models can decompactify. The most interesting thing about these pockets is that they are only allowed under certain conditions. Namely the cosmological constant and the curva- ture have to be strictly positive, and there must exist background electromagnetic fluxes. Using these conditions we tried some compactifications, but none were suc- cessful. However we investigated only a tiny region in the space of all possible compactifications, therefore the mechanism proposed in this thesis remains very promising and should be investigated further. iii Summary in layman’s terms The Standard Model of particle physics is our best tested scientific theory, however it does not incorporate gravity. Therefore a lot of physicist are searching for new theories extending the Standard Model, and the best candidate at the time of writing is superstring theory. For this theory to be mathematically consistent extra dimensions, besides the three spatial dimensions we are used to, need to be introduced. Because we did not observe any extra dimensions yet, those have to be extremely small such that they are hidden from us. This idea of extra super tiny dimensions seems very strange and unnatural. Our observable universe is a ball with a radius of about thirteen billion light years, the size of the extra dimensions has to be much smaller than a billionth of the size of an atom otherwise we would have detected them. If these extra dimensions are really there, why is there such a difference between these and the dimensions we live in? This is the question which drives the research preformed in this thesis. The most natural situation for the universe to be in is the situation were all dimensions are treated on an equal footing, hence we expect that all dimensions are either large or small. We know that our universe grew in size after the big bang, and thus we expect that around that time all dimensions were small. For this reason we take the natural situation to be that all dimensions are small. Therefore we want to find solutions to our equations which describe a universe were all dimensions are compact, but were some can spontaneously grow large. If this can be found, we discovered a potential mechanism which takes us from a natural situation, to the unnatural situation we find ourselves in. This could potentially explain why there is such a difference between the dimensions we live in, and those that are hidden from us. How do we achieve this? We reversed the above reasoning and started from a universe like ours, one which has three large dimensions and were the others are compact. We then try to fold up the three remaining dimensions, to obtain the situation were all the dimensions are of comparable size. If these three dimensions can unfold, then they will probably unfold to the universe we used to construct this model, and by this demonstrate that you can evolve from a natural to an unnatural situation. We discovered that under certain assumptions the mechanism we propose is possible. What is interesting is that for it to be possible, the universes we fold up have to meet certain conditions. These are that the three large dimensions have to be positively curved, that we need to be able to fill the universe with electromagnetic fields, and that they have to posses a positive cosmological constant. These are all things which are possible in our universe, hence this is encouraging.
Load more

Recommended publications
  • Conformal Symmetry in Field Theory and in Quantum Gravity
    universe Review Conformal Symmetry in Field Theory and in Quantum Gravity Lesław Rachwał Instituto de Física, Universidade de Brasília, Brasília DF 70910-900, Brazil; [email protected] Received: 29 August 2018; Accepted: 9 November 2018; Published: 15 November 2018 Abstract: Conformal symmetry always played an important role in field theory (both quantum and classical) and in gravity. We present construction of quantum conformal gravity and discuss its features regarding scattering amplitudes and quantum effective action. First, the long and complicated story of UV-divergences is recalled. With the development of UV-finite higher derivative (or non-local) gravitational theory, all problems with infinities and spacetime singularities might be completely solved. Moreover, the non-local quantum conformal theory reveals itself to be ghost-free, so the unitarity of the theory should be safe. After the construction of UV-finite theory, we focused on making it manifestly conformally invariant using the dilaton trick. We also argue that in this class of theories conformal anomaly can be taken to vanish by fine-tuning the couplings. As applications of this theory, the constraints of the conformal symmetry on the form of the effective action and on the scattering amplitudes are shown. We also remark about the preservation of the unitarity bound for scattering. Finally, the old model of conformal supergravity by Fradkin and Tseytlin is briefly presented. Keywords: quantum gravity; conformal gravity; quantum field theory; non-local gravity; super- renormalizable gravity; UV-finite gravity; conformal anomaly; scattering amplitudes; conformal symmetry; conformal supergravity 1. Introduction From the beginning of research on theories enjoying invariance under local spacetime-dependent transformations, conformal symmetry played a pivotal role—first introduced by Weyl related changes of meters to measure distances (and also due to relativity changes of periods of clocks to measure time intervals).
    [Show full text]
  • ABSTRACT Investigation Into Compactified Dimensions: Casimir
    ABSTRACT Investigation into Compactified Dimensions: Casimir Energies and Phenomenological Aspects Richard K. Obousy, Ph.D. Chairperson: Gerald B. Cleaver, Ph.D. The primary focus of this dissertation is the study of the Casimir effect and the possibility that this phenomenon may serve as a mechanism to mediate higher dimensional stability, and also as a possible mechanism for creating a small but non- zero vacuum energy density. In chapter one we review the nature of the quantum vacuum and discuss the different contributions to the vacuum energy density arising from different sectors of the standard model. Next, in chapter two, we discuss cosmology and the introduction of the cosmological constant into Einstein's field equations. In chapter three we explore the Casimir effect and study a number of mathematical techniques used to obtain a finite physical result for the Casimir energy. We also review the experiments that have verified the Casimir force. In chapter four we discuss the introduction of extra dimensions into physics. We begin by reviewing Kaluza Klein theory, and then discuss three popular higher dimensional models: bosonic string theory, large extra dimensions and warped extra dimensions. Chapter five is devoted to an original derivation of the Casimir energy we derived for the scenario of a higher dimensional vector field coupled to a scalar field in the fifth dimension. In chapter six we explore a range of vacuum scenarios and discuss research we have performed regarding moduli stability. Chapter seven explores a novel approach to spacecraft propulsion we have proposed based on the idea of manipulating the extra dimensions of string/M theory.
    [Show full text]
  • Weyl Gauge-Vector and Complex Dilaton Scalar for Conformal Symmetry and Its Breaking
    1 Weyl gauge-vector and complex dilaton scalar for conformal symmetry and its breaking Hans C. Ohanian1 Abstract Instead of the scalar “dilaton” field that is usually adopted to construct conformally invariant Lagrangians for gravitation, we here propose a hybrid construction, involving both a complex dilaton scalar and a Weyl gauge- vector, in accord with Weyl’s original concept of a non-Riemannian conformal geometry with a transport law for length and time intervals, for which this gauge vector is required. Such a hybrid construction permits us to avoid the wrong sign of the dilaton kinetic term (the ghost problem) that afflicts the usual construction. The introduction of a Weyl gauge-vector and its interaction with the dilaton also has the collateral benefit of providing an explicit mechanism for spontaneous breaking of the conformal symmetry, whereby the dilaton and the Weyl gauge-vector acquire masses somewhat smaller than mP by the Coleman-Weinberg mechanism. Conformal symmetry breaking is assumed to precede inflation, which occurs later by a separate GUT or electroweak symmetry breaking, as in inflationary models based on the Higgs boson. Keywords Quantum gravity • Conformal invariance • Spontaneous symmetry breaking •Weyl length transport Publication history First arXiv publication [v1] 30 January 2015. The final publication is available at Springer via http://dx.doi.org/10.1007/s10714-016-2023-8 and in General Relativity and Gravitation, March 2016, 48:25. 1 Introduction Modifications of Einstein’s gravitational theory that incorporate local conformal symmetry—that is, invariance 2 (x ) under the transformation g( x ) e g ( x ) , where ()x is an arbitrary real function—have been exploited in attempts at the solution of various of theoretical problems, such as renormalization of the stress tensor, renormalization of quantum gravity, quantum mechanics of black holes, analytic solutions and geodesic completeness in the early universe, and the dynamics that lead to inflation by symmetry breaking.
    [Show full text]
  • Conformally Invariant Equations for Graviton 50 5.1 the Conformally Invariant System of Conformal Degree 1
    Conformally Invariant Equations for Graviton Mohsen Fathi Department of Physics, Tehran Central Branch Islamic Azad Univeristy arXiv:1210.3436v3 [physics.gen-ph] 12 Nov 2012 A thesis submitted for the Master degree Master of Science in Physics Tehran, Winter 2010 I am grateful to my supervisor Dr. Mohammad Reza Tanhayi for the helps, supports and scientific training, during this work and thereafter. Abstract Recent astrophysical data indicate that our universe might currently be in a de Sitter (dS) phase. The importance of dS space has been primarily ignited by the study of the inflationary model of the universe and the quantum gravity. As we know Einstein’s theory of gravitation (with a nonzero cosmological constant) can be interpreted as a theory of a metric field; that is, a symmetric tensor field of rank-2 on a fixed de Sitter back- ground. It has been shown the massless spin-2 Fierz-Pauli wave equation (or the linearized Einstein equation) is not conformally invariant. This result is in contrary with what we used to expect for massless theories. In this thesis we obtain conformally invariant wave equation for the massless spin-2 in the dS space. This study is motivated by the belief that confor- mal invariance may be the key to a future theory of quantum gravity. Contents Introduction 1 1 The Lorentz and the conformal groups, and the concept of invari- ance 3 1.1 Grouptheory ............................... 3 1.1.1 Orthogonalgroups ........................ 4 1.1.2 Rotationgroups.......................... 5 1.2 Invarianceunderagroupaction . 7 1.2.1 Invarianceofthelawsofphysics. 7 1.3 TheLorentzgroup ............................ 8 1.4 Theconformalgroup ..........................
    [Show full text]
  • Conformal Gravity Holography in Four Dimensions
    Loyola University Chicago Loyola eCommons Physics: Faculty Publications and Other Works Faculty Publications 2014 Conformal Gravity Holography in Four Dimensions Daniel Grumiller Maria Irakleidou Iva Lovrekovic, Robert McNees Loyola University Chicago, [email protected] Follow this and additional works at: https://ecommons.luc.edu/physics_facpubs Part of the Physics Commons Recommended Citation Grumiller, D, M Irakleidou, I Lovrekovic, and R McNees. "Conformal Gravity Holography in Four Dimensions." Physical Review Letters 112, 2014. This Article is brought to you for free and open access by the Faculty Publications at Loyola eCommons. It has been accepted for inclusion in Physics: Faculty Publications and Other Works by an authorized administrator of Loyola eCommons. For more information, please contact [email protected]. This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License. © 2014 American Physical Society. week ending PRL 112, 111102 (2014) PHYSICAL REVIEW LETTERS 21 MARCH 2014 Conformal Gravity Holography in Four Dimensions † ‡ Daniel Grumiller,1,* Maria Irakleidou,1, Iva Lovrekovic,1, and Robert McNees2,§ 1Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8–10/136, A-1040 Vienna, Austria 2Department of Physics, Loyola University Chicago, Chicago, Illinois 60660, USA (Received 8 October 2013; published 18 March 2014) We formulate four-dimensional conformal gravity with (anti–)de Sitter boundary conditions that are weaker than Starobinsky boundary conditions, allowing for an asymptotically subleading Rindler term concurrent with a recent model for gravity at large distances. We prove the consistency of the variational principle and derive the holographic response functions. One of them is the conformal gravity version of the Brown–York stress tensor, the other is a “partially massless response”.
    [Show full text]
  • Rotating Black Holes in Conformal Gravity
    European Online Journal of Natural and Social Sciences 2014; www.european-science.com Vol.3, No.4 pp. 892-896 ISSN 1805-3602 Rotating black holes in conformal gravity Sara Dastan1*, Ali Farokhtabar1, Mohammad Ali Ganjali1,2, Bahare Hosseini1 1Department of Science, Faculty of Physics, Kharazmi University, Tehran, Iran 2Institute for Research in Fundamental Sciences(IPM), P.O. Box 19395-5531, Tehran, Iran *E-mail: [email protected] Received for publication: 02 June 2014. Accepted for publication: 30 September 2014. Abstract It is a long time since the motion of astronomical objects has been explained in the framework of Newtonian gravity. The great success of Newton’s law of universal gravitation in planetary motion persuaded astronomers to use this regime as a viable framework in the larger scales. Meanwhile, whenever a deviation of observed motions from expected ones were observed, the immediate question came up: should such anomalies be considered as incompleteness of laws of gravitation or as indication of the existence of unseen objects? In following we explain rotating black holes and solving this metric’s black hole with conformal gravity. Firstly explaining problem with DM then introducing conformal transformation and conformal gravity, in the last step we solve a metric for rotating black hole in the presence and absence of matter. Keywords: Rotation, Gravity, Black Holes, Conformal Gravity Introduction During the last century Einstein gravity (EG) was one the corner of theoretical physics. Despite of the success in explanation of various gravitational phenomena in nature, there are some unsolved basic problems such as singularity problem, black hole physics,… and most importantly quantum theory of gravity.
    [Show full text]
  • D-Branes in Topological Membranes
    OUTP/03–21P HWM–03–14 EMPG–03–13 hep-th/0308101 August 2003 D-BRANES IN TOPOLOGICAL MEMBRANES P. Castelo Ferreira Dep. de Matem´atica – Instituto Superior T´ecnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal and PACT – University of Sussex, Falmer, Brighton BN1 9QJ, U.K. [email protected] I.I. Kogan Dept. of Physics, Theoretical Physics – University of Oxford, Oxford OX1 3NP, U.K. R.J. Szabo Dept. of Mathematics – Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, U.K. [email protected] Abstract arXiv:hep-th/0308101v1 15 Aug 2003 It is shown how two-dimensional states corresponding to D-branes arise in orbifolds of topologically massive gauge and gravity theories. Brane vertex operators naturally appear in induced worldsheet actions when the three-dimensional gauge theory is minimally coupled to external charged matter and the orbifold relations are carefully taken into account. Boundary states corresponding to D-branes are given by vacuum wavefunctionals of the gauge theory in the presence of the matter, and their various constraints, such as the Cardy condition, are shown to arise through compatibility relations between the orbifold charges and bulk gauge invariance. We show that with a further conformally-invariant coupling to a dynamical massless scalar field theory in three dimensions, the brane tension is naturally set by the bulk mass scales and arises through dynamical mechanisms. As an auxilliary result, we show how to describe string descendent states in the three-dimensional theory through the construction of gauge-invariant excited wavefunctionals. Contents 1 INTRODUCTION AND SUMMARY 1 1.1 D-Branes ....................................
    [Show full text]
  • Universit`A Degli Studi Di Padova
    UNIVERSITA` DEGLI STUDI DI PADOVA Dipartimento di Fisica e Astronomia “Galileo Galilei” Corso di Laurea Magistrale in Fisica Tesi di Laurea Finite symmetry groups and orbifolds of two-dimensional toroidal conformal field theories Relatore Laureando Prof. Roberto Volpato Tommaso Macrelli Anno Accademico 2017/2018 Contents Introduction 5 1 Introduction to two dimensional Conformal Field Theory 7 1.1 The conformal group . .7 1.1.1 Conformal group in two dimensions . .9 1.2 Conformal invariance in two dimensions . 12 1.2.1 Fields and correlation functions . 12 1.2.2 Stress-energy tensor and conformal transformations . 13 1.2.3 Operator formalism: radial quantization . 14 1.3 General structure of a Conformal Field Theory in two dimensions . 16 1.3.1 Meromorphic Conformal Field Theory . 18 1.4 Examples . 22 1.4.1 Free boson . 22 1.4.2 Free Majorana fermion . 26 1.4.3 Ghost system . 27 2 Elements of String and Superstring Theory 28 2.1 Bosonic String Theory . 29 2.1.1 Classical Bosonic String . 29 2.1.2 Quantization . 31 2.1.3 BRST symmetry and Hilbert Space . 33 2.1.4 Spectrum of the Bosonic String . 34 2.1.5 What’s wrong with Bosonic String? . 36 2.2 Superstring Theory . 37 2.2.1 Introduction to Superstrings . 37 2.2.2 Heterotic String . 39 3 Compactifications of String Theory 41 3.1 An introduction: Kaluza-Klein compactification . 42 3.2 Free boson compactified on a circle . 43 3.2.1 Closed strings and T-Duality . 45 3.2.2 Enhanced symmetries at self-dual radius .
    [Show full text]
  • Conformally Coupled General Relativity
    universe Article Conformally Coupled General Relativity Andrej Arbuzov 1,* and Boris Latosh 2 ID 1 Bogoliubov Laboratory for Theoretical Physics, JINR, Dubna 141980, Russia 2 Dubna State University, Department of Fundamental Problems of Microworld Physics, Universitetskaya str. 19, Dubna 141982, Russia; [email protected] * Correspondence: [email protected] Received: 28 December 2017; Accepted: 7 February 2018; Published: 14 February 2018 Abstract: The gravity model developed in the series of papers (Arbuzov et al. 2009; 2010), (Pervushin et al. 2012) is revisited. The model is based on the Ogievetsky theorem, which specifies the structure of the general coordinate transformation group. The theorem is implemented in the context of the Noether theorem with the use of the nonlinear representation technique. The canonical quantization is performed with the use of reparametrization-invariant time and Arnowitt– Deser–Misner foliation techniques. Basic quantum features of the models are discussed. Mistakes appearing in the previous papers are corrected. Keywords: models of quantum gravity; spacetime symmetries; higher spin symmetry 1. Introduction General relativity forms our understanding of spacetime. It is verified by the Solar System and cosmological tests [1,2]. The recent discovery of gravitational waves provided further evidence supporting the theory’s viability in the classical regime [3–6]. Despite these successes, there are reasons to believe that general relativity is unable to provide an adequate description of gravitational phenomena in the high energy regime and should be either modified or replaced by a new theory of gravity [7–11]. One of the main issues is the phenomenon of inflation. It appears that an inflationary phase of expansion is necessary for a self-consistent cosmological model [12–14].
    [Show full text]
  • Gravitational Waves in Massive Conformal Gravity Arxiv:2007.03637V2 [Gr-Qc] 23 Jul 2020
    Gravitational waves in massive conformal gravity F. F. Faria ∗ Centro de Ci^enciasda Natureza, Universidade Estadual do Piau´ı, 64002-150 Teresina, PI, Brazil Abstract First, we obtain the plane wave solution of the linearized massive conformal gravity field equations. It is shown that the theory has seven physical plane waves. In addition, we investigate the gravitational radiation from binary systems in massive conformal gravity. We find that the theory with large graviton mass can reproduce the orbit of binaries by the emission of gravitational waves. arXiv:2007.03637v2 [gr-qc] 23 Jul 2020 PACS numbers: 04.50.Kd, 04.30.-w * [email protected] 1 Introduction Over the years several alternative theories of gravity have emerged in the attempt to solve some of the problems presented by the general theory of rel- ativity, such as the dark matter and dark energy problems. Besides solving these problems, for an alternative theory of gravity to be considered consis- tent, it must also reproduce the successful predictions of general relativity. One of these recently confirmed predictions is the existence of gravitational waves [1, 2, 3, 4]. Among the many alternative theories of gravity that have already studied the gravitational waves phenomenology is conformal gravity (CG). It was shown that the plane wave of this theory is composed of the usual plane wave of general relativity plus a plane wave that grows linearly in time [5], which causes the energy carried by the CG plane wave to diverges in momentum space [6]. In this paper, we intend to study the behavior of gravitational waves in another alternative theory of gravity with conformal symmetry called massive conformal gravity (MCG) [7].
    [Show full text]
  • Conformal Gravity and the Alcubierre Warp Drive Metric
    Physics Faculty Works Seaver College of Science and Engineering 2013 Conformal Gravity and the Alcubierre Warp Drive Metric Gabriele U. Varieschi Loyola Marymount University, [email protected] Zily Burstein Loyola Marymount University Follow this and additional works at: https://digitalcommons.lmu.edu/phys_fac Part of the Physics Commons Recommended Citation Gabriele U. Varieschi and Zily Burstein, “Conformal Gravity and the Alcubierre Warp Drive Metric,” ISRN Astronomy and Astrophysics, vol. 2013, Article ID 482734, 13 pages, 2013. doi: 10.1155/2013/482734 This Article is brought to you for free and open access by the Seaver College of Science and Engineering at Digital Commons @ Loyola Marymount University and Loyola Law School. It has been accepted for inclusion in Physics Faculty Works by an authorized administrator of Digital Commons@Loyola Marymount University and Loyola Law School. For more information, please contact [email protected]. Hindawi Publishing Corporation ISRN Astronomy and Astrophysics Volume 2013, Article ID 482734, 13 pages http://dx.doi.org/10.1155/2013/482734 Research Article Conformal Gravity and the Alcubierre Warp Drive Metric Gabriele U. Varieschi and Zily Burstein Department of Physics, Loyola Marymount University, Los Angeles, CA 90045, USA Correspondence should be addressed to Gabriele U. Varieschi; [email protected] Received 7 November 2012; Accepted 24 November 2012 Academic Editors: P. P. Avelino, R. N. Henriksen, and P. A. Hughes Copyright © 2013 G. U. Varieschi and Z. Burstein. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
    [Show full text]
  • Free Lunch from T-Duality
    Free Lunch from T-Duality Ulrich Theis Institute for Theoretical Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, D{07743 Jena, Germany [email protected] We consider a simple method of generating solutions to Einstein gravity coupled to a dilaton and a 2-form gauge potential in n dimensions, starting from an arbitrary (n m)- − dimensional Ricci-flat metric with m commuting Killing vectors. It essentially consists of a particular combination of coordinate transformations and T-duality and is related to the so-called null Melvin twists and TsT transformations. Examples obtained in this way include two charged black strings in five dimensions and a finite action configuration in three dimensions derived from empty flat space. The latter leads us to amend the effective action by a specific boundary term required for it to admit solutions with positive action. An extension of our method involving an S-duality transformation that is applicable to four-dimensional seed metrics produces further nontrivial solutions in five dimensions. 1 Introduction One of the most attractive features of string theory is that it gives rise to gravity: the low-energy effective action for the background fields on a string world-sheet is diffeomor- phism invariant and includes the Einstein-Hilbert term of general relativity. This effective action is obtained by integrating renormalization group beta functions whose vanishing is required for Weyl invariance of the world-sheet sigma model and can be interpreted as a set of equations of motion for the background fields. Solutions to these equations determine spacetimes in which the string propagates.
    [Show full text]