Conformal Symmetry in Field Theory and in Quantum Gravity
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Renormalization Group Flows from Holography; Supersymmetry and a C-Theorem
© 1999 International Press Adv. Theor. Math. Phys. 3 (1999) 363-417 Renormalization Group Flows from Holography; Supersymmetry and a c-Theorem D. Z. Freedmana, S. S. Gubser6, K. Pilchc and N. P. Warnerd aDepartment of Mathematics and Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139 b Department of Physics, Harvard University, Cambridge, MA 02138, USA c Department of Physics and Astronomy, University of Southern California, Los Angeles, CA 90089-0484, USA d Theory Division, CERN, CH-1211 Geneva 23, Switzerland Abstract We obtain first order equations that determine a super symmetric kink solution in five-dimensional Af = 8 gauged supergravity. The kink interpo- lates between an exterior anti-de Sitter region with maximal supersymme- try and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in J\f = 4 super-Yang-Mills theory broken to an Af = 1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed cor- respondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new Af = 4 gauged supergravity theory holographically dual to a sector of Af = 2 gauge theories based on quiver diagrams. e-print archive: http.y/xxx.lanl.gov/abs/hep-th/9904017 *On leave from Department of Physics and Astronomy, USC, Los Angeles, CA 90089 364 RENORMALIZATION GROUP FLOWS We consider more general kink geometries and construct a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. -
Spectra of Conformal Sigma Models
Spectra of Conformal Sigma Models Dissertation zur Erlangung des Doktorgrades an der Fakultät für Mathematik, Informatik und Naturwissenschaften Fachbereich Physik der Universität Hamburg vorgelegt von Václav Tlapák aus Berlin Hamburg 2014 Tag der Disputation: 30. Januar 2015 Folgende Gutachter empfehlen die Annahme der Dissertation: Prof. Dr. Volker Schomerus Prof. Dr. Gleb Arutyunov Zusammenfassung Die vorliegende Arbeit beschäftigt sich mit den Spektren von konformen Sigma Modellen, die auf (verallgemeinerten) symmetrischen Räumen defi- niert sind. Die Räume, auf denen Sigma Modelle ohne Wess-Zumino-Term konform sind, sind Supermannigfaltigkeiten, also Mannigfaltigkeiten, die fermionische Richtungen aufweisen. Wir stellen die Konstruktion von Ver- tex Operatoren vor, gefolgt von der Hintergrundfeld-Entwicklung. Für semi- symmetrische Räume berechnen wir anschließend die diagonalen Terme der anomalen Dimensionen dieser Operatoren in führender Ordnung. Das Resul- tat stimmt mit dem für symmetrische Räume überein, jedoch treten nicht- diagonale Terme auf, die hier nicht weiter betrachtet werden. Anschließend präsentieren wir eine detaillierte Analyse des Spectrums des Supersphären S3j2 Sigma Modells. Dies ist eins der einfachsten Beispie- le für konforme Sigma Modelle auf symmetrischen Räumen und dient als Illustration für die Mächtigkeit der vorgestellten Methoden. Wir verwenden die erhaltenen Daten, um eine Dualität mit dem OSP(4j2) Gross-Neveu Modell zu untersuchen, die von Candu und Saleur vorgeschlagen wurde. Wir verwenden dazu ein Resultat, welches die anomalen Dimensionen von 1 2 BPS Operatoren zu allen Ordnungen berechnet. Wir finden das gesamte Grundzustandsspektrum des Sigma Modells. Darüber hinaus legen wir dar, dass sowohl die Zwangsbedingungen als auch die Bewegungsgleichungen des Sigma Modells korrekt vom Gross-Neveu Modell implementiert werden. Die Dualität wird weiterhin durch ein neues exaktes Resultat für die anomalen Dimensionen der Grundzustände unterstützt. -
Simulating Quantum Field Theory with a Quantum Computer
Simulating quantum field theory with a quantum computer John Preskill Lattice 2018 28 July 2018 This talk has two parts (1) Near-term prospects for quantum computing. (2) Opportunities in quantum simulation of quantum field theory. Exascale digital computers will advance our knowledge of QCD, but some challenges will remain, especially concerning real-time evolution and properties of nuclear matter and quark-gluon plasma at nonzero temperature and chemical potential. Digital computers may never be able to address these (and other) problems; quantum computers will solve them eventually, though I’m not sure when. The physics payoff may still be far away, but today’s research can hasten the arrival of a new era in which quantum simulation fuels progress in fundamental physics. Frontiers of Physics short distance long distance complexity Higgs boson Large scale structure “More is different” Neutrino masses Cosmic microwave Many-body entanglement background Supersymmetry Phases of quantum Dark matter matter Quantum gravity Dark energy Quantum computing String theory Gravitational waves Quantum spacetime particle collision molecular chemistry entangled electrons A quantum computer can simulate efficiently any physical process that occurs in Nature. (Maybe. We don’t actually know for sure.) superconductor black hole early universe Two fundamental ideas (1) Quantum complexity Why we think quantum computing is powerful. (2) Quantum error correction Why we think quantum computing is scalable. A complete description of a typical quantum state of just 300 qubits requires more bits than the number of atoms in the visible universe. Why we think quantum computing is powerful We know examples of problems that can be solved efficiently by a quantum computer, where we believe the problems are hard for classical computers. -
Durham Research Online
Durham Research Online Deposited in DRO: 30 January 2017 Version of attached le: Published Version Peer-review status of attached le: Peer-reviewed Citation for published item: Bhattacharya, Jyotirmoy and Lipstein, Arthur E. (2016) '6d dual conformal symmetry and minimal volumes in AdS.', Journal of high energy physics., 2016 (12). p. 105. Further information on publisher's website: https://doi.org/10.1007/JHEP12(2016)105 Publisher's copyright statement: Open Access, c The Authors. Article funded by SCOAP3. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. 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 Published for SISSA by Springer Received: November 16, 2016 Revised: December 8, 2016 Accepted: December 12, 2016 Published: December 20, 2016 6d dual conformal symmetry and minimal volumes JHEP12(2016)105 in AdS Jyotirmoy Bhattacharya and Arthur E. -
Kaluza-Klein Gravity, Concentrating on the General Rel- Ativity, Rather Than Particle Physics Side of the Subject
Kaluza-Klein Gravity J. M. Overduin Department of Physics and Astronomy, University of Victoria, P.O. Box 3055, Victoria, British Columbia, Canada, V8W 3P6 and P. S. Wesson Department of Physics, University of Waterloo, Ontario, Canada N2L 3G1 and Gravity Probe-B, Hansen Physics Laboratories, Stanford University, Stanford, California, U.S.A. 94305 Abstract We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identi- fied and contrasted: compactified, projective and noncompactified. We discuss the cosmological and astrophysical implications of extra dimensions, and conclude that none of the three approaches can be ruled out on observational grounds at the present time. arXiv:gr-qc/9805018v1 7 May 1998 Preprint submitted to Elsevier Preprint 3 February 2008 1 Introduction Kaluza’s [1] achievement was to show that five-dimensional general relativity contains both Einstein’s four-dimensional theory of gravity and Maxwell’s the- ory of electromagnetism. He however imposed a somewhat artificial restriction (the cylinder condition) on the coordinates, essentially barring the fifth one a priori from making a direct appearance in the laws of physics. Klein’s [2] con- tribution was to make this restriction less artificial by suggesting a plausible physical basis for it in compactification of the fifth dimension. This idea was enthusiastically received by unified-field theorists, and when the time came to include the strong and weak forces by extending Kaluza’s mechanism to higher dimensions, it was assumed that these too would be compact. This line of thinking has led through eleven-dimensional supergravity theories in the 1980s to the current favorite contenders for a possible “theory of everything,” ten-dimensional superstrings. -
Effective Quantum Field Theories Thomas Mannel Theoretical Physics I (Particle Physics) University of Siegen, Siegen, Germany
Generating Functionals Functional Integration Renormalization Introduction to Effective Quantum Field Theories Thomas Mannel Theoretical Physics I (Particle Physics) University of Siegen, Siegen, Germany 2nd Autumn School on High Energy Physics and Quantum Field Theory Yerevan, Armenia, 6-10 October, 2014 T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Overview Lecture 1: Basics of Quantum Field Theory Generating Functionals Functional Integration Perturbation Theory Renormalization Lecture 2: Effective Field Thoeries Effective Actions Effective Lagrangians Identifying relevant degrees of freedom Renormalization and Renormalization Group T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Lecture 3: Examples @ work From Standard Model to Fermi Theory From QCD to Heavy Quark Effective Theory From QCD to Chiral Perturbation Theory From New Physics to the Standard Model Lecture 4: Limitations: When Effective Field Theories become ineffective Dispersion theory and effective field theory Bound Systems of Quarks and anomalous thresholds When quarks are needed in QCD É. T. Mannel, Siegen University Effective Quantum Field Theories: Lecture 1 Generating Functionals Functional Integration Renormalization Lecture 1: Basics of Quantum Field Theory Thomas Mannel Theoretische Physik I, Universität Siegen f q f et Yerevan, October 2014 T. Mannel, Siegen University Effective Quantum -
Conformal Theory of Everything (CTOE)
Conformal theory of everything F. F. Faria ∗ Centro de Ciˆencias da Natureza, Universidade Estadual do Piau´ı, 64002-150 Teresina, PI, Brazil Abstract By using conformal symmetry we unify the standard model of par- ticle physics with gravity in a consistent quantum field theory which describes all the fundamental particles and forces of nature. arXiv:1903.04893v3 [hep-ph] 26 Feb 2020 PACS numbers: 104.60.-m, 98.80.-k, 04.50.+h * [email protected] 1 Introduction It is well know that the standard model (SM) of particle physics is consistent with the experiments performed so far on particle accelerators such as the large hadron collider (LHC). However, the theory presents some problems such as the hierarchy and the Landau pole problems. Several modifications of the SM at scales between the electroweak and Planck scales, such as GUT [1, 2, 3, 4] or SUSY [5, 6, 7, 8, 9, 10, 11, 12, 13], have been proposed to solve such problems. However, it is likely that there is no new physics beyond the SM all the way up to the Planck scale [14]. This leads us to suppose that the SM is a low energy limit of a fundamental theory defined at the Planck scale. Since gravitational effects are expected to be important around the Planck scale, it is natural to conjecture that this fundamental theory includes quantum gravity. One of the most straightforward ways to extend and unify physical the- ories is to change the symmetry of their actions. A strong candidate to be incorporated in the unification of the SM with gravity is the (local) conformal symmetry, which performs a multiplicative rescaling of all fields according to Φ=Ω(˜ x)−∆Φ Φ, (1) where Ω(x) is an arbitrary function of the spacetime coordinates, and ∆Φ is the scaling dimension of the field Φ, whose values are 2 for the metric field, 0 for gauge bosons, 1 for scalar fields, and 3/2 for fermions.− The consideration of the conformal symmetry as one of the fundamen- tal symmetries of physics is justified for several reasons. -
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. -
Gravity, Inertia, and Quantum Vacuum Zero Point Fields
Foundations of Physics, Vol.31,No. 5, 2001 Gravity, Inertia, and Quantum Vacuum Zero Point Fields James F. Woodward1 Received July 27, 2000 Over the past several years Haisch, Rueda, and others have made the claim that the origin of inertial reaction forces can be explained as the interaction of electri- cally charged elementary particles with the vacuum electromagnetic zero-point field expected on the basis of quantum field theory. After pointing out that this claim, in light of the fact that the inertial masses of the hadrons reside in the electrically chargeless, photon-like gluons that bind their constituent quarks, is untenable, the question of the role of quantum zero-point fields generally in the origin of inertia is explored. It is shown that, although non-gravitational zero-point fields might be the cause of the gravitational properties of normal matter, the action of non-gravitational zero-point fields cannot be the cause of inertial reac- tion forces. The gravitational origin of inertial reaction forces is then briefly revisited. Recent claims critical of the gravitational origin of inertial reaction forces by Haisch and his collaborators are then shown to be without merit. 1. INTRODUCTION Several years ago Haisch, Rueda, and Puthoff (1) (hereafter, HRP) pub- lished a lengthy paper in which they claimed that a substantial part, indeed perhaps all of normal inertial reaction forces could be understood as the action of the electromagnetic zero-point field (EZPF), expected on the basis of quantum field theory, on electric charges of normal matter. In several subsequent papers Haisch and Rueda particularly have pressed this claim, making various modifications to the fundamental argument to try to deflect several criticisms. -
Loop Quantum Cosmology, Modified Gravity and Extra Dimensions
universe Review Loop Quantum Cosmology, Modified Gravity and Extra Dimensions Xiangdong Zhang Department of Physics, South China University of Technology, Guangzhou 510641, China; [email protected] Academic Editor: Jaume Haro Received: 24 May 2016; Accepted: 2 August 2016; Published: 10 August 2016 Abstract: Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans–Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed. Keywords: loop quantum cosmology; singularity resolution; effective equation 1. Introduction Loop quantum gravity (LQG) is a quantum gravity scheme that tries to quantize general relativity (GR) with the nonperturbative techniques consistently [1–4]. Many issues of LQG have been carried out in the past thirty years. In particular, among these issues, loop quantum cosmology (LQC), which is the cosmological sector of LQG has received increasing interest and has become one of the most thriving and fruitful directions of LQG [5–9]. It is well known that GR suffers singularity problems and this, in turn, implies that our universe also has an infinitely dense singularity point that is highly unphysical. -
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 .......................... -
Twenty Years of the Weyl Anomaly
CTP-TAMU-06/93 Twenty Years of the Weyl Anomaly † M. J. Duff ‡ Center for Theoretical Physics Physics Department Texas A & M University College Station, Texas 77843 ABSTRACT In 1973 two Salam prot´eg´es (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor 2 gµν(x) Ω (x)gµν (x) displayed by classical massless field systems in interac- tion with→ gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic re- view. arXiv:hep-th/9308075v1 16 Aug 1993 CTP/TAMU-06/93 July 1993 †Talk given at the Salamfest, ICTP, Trieste, March 1993. ‡ Research supported in part by NSF Grant PHY-9106593. When all else fails, you can always tell the truth. Abdus Salam 1 Trieste and Oxford Twenty years ago, Derek Capper and I had embarked on our very first post- docs here in Trieste. We were two Salam students fresh from Imperial College filled with ideas about quantizing the gravitational field: a subject which at the time was pursued only by mad dogs and Englishmen. (My thesis title: Problems in the Classical and Quantum Theories of Gravitation was greeted with hoots of derision when I announced it at the Cargese Summer School en route to Trieste. The work originated with a bet between Abdus Salam and Hermann Bondi about whether you could generate the Schwarzschild solution using Feynman diagrams. You can (and I did) but I never found out if Bondi ever paid up.) Inspired by Salam, Capper and I decided to use the recently discovered dimensional regularization1 to calculate corrections to the graviton propaga- tor from closed loops of massless particles: vectors [1] and spinors [2], the former in collaboration with Leopold Halpern.