From Quantum Chromodynamics to Supergravity

Total Page:16

File Type:pdf, Size:1020Kb

From Quantum Chromodynamics to Supergravity Harmony of Scattering Amplitudes: From Quantum Chromodynamics to Supergravity BNL Physics Colloquium Nov 12, 2013 Zvi Bern, UCLA 1 Scattering amplitudes Scattering of elementary particles is fundamental to our ability to unravel microscopic laws of nature. Smooth running of the Large Hadron Collider at CERN emphasizes importance of scattering amplitudes. Vast subject. Here we give some examples of advances of past few years in understanding and calculating 4 month program at Simons Center scattering in quantum field theory. 2 Outline Will outline some new developments in understanding scattering amplitudes. Surprising harmony. 1. Scattering using Feynman diagrams. Obscures harmony. 2. Modern on-shell methods for scattering. 3. Sample applications: — LHC Physics — Reexamination of compatibility of quantum mechanics and general relativity. W q e º q g0 g g g g 3 Feynman Diagrams jets p quark p gluon jets of Higgs boson event in CMS detector hadrons Note jets of particles Quantum chromodynamics (QCD) describes the strong nuclear force binding quarks and gluons into protons and neutrons. QCD describes in great detail, scattering of protons at particle colliders. 4 Scattering Amplitudes Every graduate student in particle physics learns how to calculate scattering amplitudes via Feynman diagrams. gluon scattering Feynman propagator Coupling constant “color” factor In principle this is a complete solution for small coupling Tree – Leading Order (LO) Loop – Next-To-Leading Order (NLO) Quantum correction Feynman diagrams give us a perturbative expansion in Planck’s constant ¹h 5 Scattering Amplitudes In principle this is a complete solution for scattering with small coupling constants. Systematic! In practice not so easy: • Proper way to calculate? Many scales, large logs, infrared issues, strong coupling, non-perturbative contributions, physical states, etc. In this talk we do not address these issues. • A more practical problem is just dealing with the Feynman diagrams. In this talk we discuss this aspect. 6 State-of-the-Art Feynman Diagram Calculations In 1948 Schwinger computed anomalous magnetic moment of the electron. In 2010 typical 1-loop modern example: g : gluon -- carrier of strong force q: quark -- matter W, Z : Weak boson carrier of weak interaction 60 years later at 1 loop only 2 or 3 legs more than Schwinger if we use traditional Feynman diagrams. 7 Tree-level example: Five gluons Force carriers in QCD are gluons. Similar to photons of QED except they self interact. Consider the five-gluon amplitude: Used in calculation of pp 3 jets at CERN If you evaluate this following textbook Feynman rules you find… 8 Result of evaluation (actually only a small part of it): Messy combination of momenta and gluon polarization vectors. 9 Reconsider Five-Gluon Tree Xu, Zhang and Chang With a little Chinese magic, i.e. helicity states: and many others Use a better organization of color charges: Motivated by the color organization of open string amplitudes. 10 Mangano and Parke Example of loop difficulty Consider a tensor integral: Note: this is trivial on modern computer. Non-trivial for larger numbers of external particles. Evaluate this integral via Passarino-Veltman reduction. Result is … 11 Result of performing the integration Calculations explode for larger numbers of particles or loops. Clearly, there should be a better way! 12 W + n Jet NLO Calculations for the LHC Suppose you said “I’m going not shave until I finish calculating” W + 1 jet W + 2 jets W + 3 jets Still no Feynman diagram calculation 13 Why are Feynman diagrams difficult for high-loop or high-multiplicity processes? • Vertices and propagators involve unphysical gauge-dependent off-shell states. An important origin of the complexity. Individual Feynman diagrams unphysical Einstein’s relation between momentum and energy violated in the loops. Unphysical states! Not gauge invariant. • All steps should be in terms of gauge invariant on-shell physical states. On-shell formalism. Don’t violate Einstein’s relation! ZB, Dixon, Dunbar, Kosower (1998) 14 Heisenberg Feynman diagram loops violate on shellness because they encode the uncertainty principle. Loops: You can create new particles even with insufficient energy as long as you destroy them quickly enough. Theorem: Off-shellness or energy conservation violation is essential for getting the correct answer because of uncertainty relation. It looks like an on-shell formalism will fail to capture everything. 15 Sneaking Past Heisenberg Favorite Theorem: Theorems in physics are bound to be misleading or have major loopholes. What’s the loophole here? • Want to reconstruct the complete amplitude using only on-shell physical information. • Keep particles on shell in intermediate steps of calculation, not in final results. 16 Modern Unitarity Method on-shell ZB, Dixon, Dunbar and Kosower Two-particle cut: Systematic assembly of complete amplitudes from cuts for any number of Three-particle cut: particles or loops. ZB, Dixon and Kosower; Generalized ZB, Morgan; Britto, Cachazo, Feng; unitarity as a Ossala,Pittau,Papadopoulos; practical tool. Ellis, Kunszt, Melnikov; Forde; Badger on-shell and many others Reproduces Feynman diagrams except intermediate steps of calculation based on physical quantities not unphysical ones. 17 On-Shell Recursion for Tree Amplitudes Britto, Cachazo, Feng and Witten (BCFW) Physical scattering amplitudes constructed from on-shell physical scattering amplitudes with fewer particles! on-shell amplitude Works by making clever use of Cauchy’s residue theorem Same construction works in gravity Brandhuber, Travaglini, Spence; Cachazo, Svrcek; Benincasa, Boucher-Veronneau, Cachazo; Arkani-Hamed and Kaplan, Hall In gauge theory, extended to loops. Arkani-Hamed et al. 18 G. Salam, ICHEP 2010 19 20 G. Salam, La Thuile 2012 21 2013: NLO W+5j [BlackHat+Sherpa: Bern et al] [unitarity] BlackHat: C++ implementation of on-shell methods for one-loop amplitudes ZB, Dixon, Febres Cordero, Hoeche, Ita, Kosower, Maitre, Ozeren BlackHat is a C++ package for numerically computing one-loop matrix elements with 6 or more external particles. • Input is on-shell tree-level amplitudes. • Output is numerical on-shell one-loop amplitudes. On-shell methods used to achieve the speed and stability required for LHC phenomenology at NLO. Other (semi) on-shell packages: — Helac-NLO: Bevilacqua, Czakon, Ossola, Papadopoulos, Pittau, Worek — Rocket: Ellis, Giele, Kunszt, Melnikov, Zanderighi — SAMURAI: Mastrolia, Ossola, Reiter, Tramontano — MadLoop: Hirchi, Maltoni, Frixione, Frederix, Garzelli, Pittau — GoSam: Cullen, Greiner, Heinrich, Luisoni, Mastrolia, Ossola, Reiter, Tramontano — NGluon: Badger, Biedermann, Uwer 22 ATLAS Comparison against NLO ATLAS compared data against NLO theoretical predictions Powerful experimental confirmation of NLO approach. Validate in regions where no new physics is expected and look for discrepancies on tails of distributions where new physics may be hiding. number of jets Theory predictions from BlackHat used to aid search for supersymmetry. W +1, 2, 3, 4 jets inclusive 23 W + 5 Jets in NLO QCD Hadronic energy spectrum A triumph for on-shell methods! Recently completed. arXiv:1304.1253 LO/NLO ratio LO/NLO W q e Transverse hadronic energy º q • A new level for “state-of-the-art” LHC theory: First NLOg0 QCD 2 6 process. g g g g Examples of Harmony in Scattering Amplitudes 25 Gravity vs Gauge Theory Consider the Einstein gravity Lagrangian curvature Flat-space metric graviton field metric Infinite number of complicated interactions + … terrible mess Compare to gauge-theory Lagrangian on which QCD is based Only three and four point interactions Gravity seems so much more complicated than gauge theory. Does not look harmonious! 26 Three Vertices Standard Feynman diagram approach. Three-gluon vertex: Three-graviton vertex: About 100 terms in three vertex Naïve conclusion: Gravity is a nasty mess. Where is the harmony? 27 Simplicity of Gravity Amplitudes People were looking at gravity the wrong way. On-shell viewpoint much more powerful. On-shell three vertices contains all information: gauge theory: “square” of gravity: Yang-Mills vertex. Using modern methods, any gravity scattering amplitude constructible solely from on-shell 3 vertex. Higher-point vertices irrelevant! Harmony is revealed! 28 Gravity vs Gauge Theory Consider the Einstein gravity Lagrangian flat metric graviton field metric Infinite number of irrelevant interactions! Simple relation + … to gauge theory Compare to gauge-theory Lagrangian on which QCD is based. Only three-point interactions no Gravity seems so much more complicated than gauge theory. Does not look harmonious! 29 Duality Between Color and Kinematics momentum dependent coupling color factor kinematic factor constant Color factors based on a Lie algebra: Jacobi Identity Use 1 = s/s = t/t = u/u to assign 4-point diagram to others. n c n c n c tree = g2 s s + t t + u u A4 s t u ³ ´ Color factors satisfy Jacobi identity: Numerator factors satisfy similar identity: Color and kinematics sing the same tune! 30 Duality Between Color and Kinematics Consider five-point tree amplitude: ZB, Carrasco, Johansson (BCJ) color factor kinematic numerator factor Feynman propagators a3a4b ba5c ca1a2 a3a4b ba2c ca1a5 a3a4b ba1c ca2a5 c1 f f f ; c2 f f f ; c3 f f f ´ ´ ´ c1 c2 + c3 = 0 n1 n2 + n3 = 0 ¡ ¡ Claim: We can always find a rearrangement so color and kinematics satisfy the same algebraic constraint equations. Recent progress on unraveling mysterious relations. BCJ, Bjerrum-Bohr, Feng,
Recommended publications
  • Curvature Tensors in a 4D Riemann–Cartan Space: Irreducible Decompositions and Superenergy
    Curvature tensors in a 4D Riemann–Cartan space: Irreducible decompositions and superenergy Jens Boos and Friedrich W. Hehl [email protected] [email protected]"oeln.de University of Alberta University of Cologne & University of Missouri (uesday, %ugust 29, 17:0. Geometric Foundations of /ravity in (artu Institute of 0hysics, University of (artu) Estonia Geometric Foundations of /ravity Geometric Foundations of /auge Theory Geometric Foundations of /auge Theory ↔ Gravity The ingredients o$ gauge theory: the e2ample o$ electrodynamics ,3,. The ingredients o$ gauge theory: the e2ample o$ electrodynamics 0henomenological Ma24ell: redundancy conserved e2ternal current 5 ,3,. The ingredients o$ gauge theory: the e2ample o$ electrodynamics 0henomenological Ma24ell: Complex spinor 6eld: redundancy invariance conserved e2ternal current 5 conserved #7,8 current ,3,. The ingredients o$ gauge theory: the e2ample o$ electrodynamics 0henomenological Ma24ell: Complex spinor 6eld: redundancy invariance conserved e2ternal current 5 conserved #7,8 current Complete, gauge-theoretical description: 9 local #7,) invariance ,3,. The ingredients o$ gauge theory: the e2ample o$ electrodynamics 0henomenological Ma24ell: iers Complex spinor 6eld: rce carr ry of fo mic theo rrent rosco rnal cu m pic en exte att desc gredundancyiv er; N ript oet ion o conserved e2ternal current 5 invariance her f curr conserved #7,8 current e n t s Complete, gauge-theoretical description: gauge theory = complete description of matter and 9 local #7,) invariance how it interacts via gauge bosons ,3,. Curvature tensors electrodynamics :ang–Mills theory /eneral Relativity 0oincaré gauge theory *3,. Curvature tensors electrodynamics :ang–Mills theory /eneral Relativity 0oincaré gauge theory *3,. Curvature tensors electrodynamics :ang–Mills theory /eneral Relativity 0oincar; gauge theory *3,.
    [Show full text]
  • Scattering in N = 4 Super Yang–Mills and N = 8 Supergravity
    Scattering in = 4 super Yang{Mills and = 8 supergravity N N Thesis by Enrico Herrmann In Partial Fulfillment of the Requirements for the degree of Doctor of Philosophy CALIFORNIA INSTITUTE OF TECHNOLOGY Pasadena, California 2017 Defended May 15, 2017 ii c 2017 Enrico Herrmann ORCID: 0000-0002-3983-2993 All rights reserved iii Acknowledgments During my time as a graduate student at Caltech I had the pleasure to interact with a number of remarkable scientists. First and foremost I would like to thank my advisor, Mark Wise, for taking me on as a graduate student during my first year at Caltech. Even more so, I am thankful that he gave me the opportunity to follow my own research interests and for all his support along the way. Mark always had an open ear and good advice concerning practical matters like organizing travel funding or navigating the academic life in general. I am grateful that he also nominated me for a Dominic Orr Fellowship, which allowed me a one year break from all teaching duties. Along with Mark, I would like to thank my co-advisor, Jaroslav Trnka, from whom I learned an enormous amount about scattering amplitudes and physics in general. I very much appreciate all his invaluable support and encouragement throughout my graduate studies. Without him and his generous help, many of my conference visits and trips would not have been possible. In all the workshops he co-organized, Jaroslav enabled young scientists to present their research. In many respects, Jaroslav is my scientific role model. In addition to the mentorship I have received by Mark and Jaroslav, I have benefited significantly from the interaction with my collaborators Zvi Bern, Jacob Bourjaily, Sean Litsey, James Stankowicz, and Jaroslav Trnka.
    [Show full text]
  • Arxiv:1108.0677V2 [Hep-Th]
    DAMTP-2011-59 MIFPA-11-34 THE SHEAR VISCOSITY TO ENTROPY RATIO: A STATUS REPORT Sera Cremonini ♣,♠ ∗ ♣ Centre for Theoretical Cosmology, DAMTP, CMS, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK ♠ George and Cynthia Mitchell Institute for Fundamental Physics and Astronomy Texas A&M University, College Station, TX 77843–4242, USA (Dated: October 22, 2018) This review highlights some of the lessons that the holographic gauge/gravity duality has taught us regarding the behavior of the shear viscosity to entropy density in strongly coupled field theories. The viscosity to entropy ratio has been shown to take on a very simple universal value in all gauge theories with an Einstein gravity dual. Here we describe the origin of this universal ratio, and focus on how it is modified by generic higher derivative corrections corresponding to curvature corrections on the gravity side of the duality. In particular, certain curvature corrections are known to push the viscosity to entropy ratio below its universal value. This disproves a longstanding conjecture that such a universal value represents a strict lower bound for any fluid in nature. We discuss the main developments that have led to insight into the violation of this bound, and consider whether the consistency of the theory is responsible for setting a fundamental lower bound on the viscosity to entropy ratio. arXiv:1108.0677v2 [hep-th] 23 Aug 2011 ∗ Electronic address: [email protected] 2 Contents I. Introduction 3 A. The quark gluon plasma and the shear viscosity to entropy ratio 4 II. The universality of η/s 6 A.
    [Show full text]
  • Scattering Amplitudes in Quantum Field Theory
    Scattering Amplitudes in Quantum Field Theory European Physical Society Meeting Stockholm July 24, 2013 Zvi Bern, UCLA W q e º q g0 g g g g 1 Outline 1) Remarkable progress in scattering amplitudes. 2) Brief summary of new advances and ideas. 3) Example: applications to LHC physics. 4) Example: A duality between color and kinematics. 5) Example: UV surprises in supergravity theories. 2 Scattering amplitudes Scattering of elementary particles is fundamental to our ability to unravel microscopic laws of nature. Arrival of the Large Hadron Collider raises importance of collider physics and scattering amplitudes. Here we give some examples of advances of past few years in understanding and calculating scattering in quantum field theory. 3 Major Advance in Scattering Amplitudes “Impossible calculations” of scattering amplitudes in gauge and gravity theories now commonplace. A few highlights from past year: • Constructing large chunks of the scattering amplitudes of N = 4 super-Yang-Mills theory, towards a full construction. Alday, Arkani-Hamed, Basso, Bourjaily, Cachazo, Caron-Huot, Dixon, Duhr, Gehrmann, Golden, Goncharov, He, Henn, Heslop, Huber, Johansson, Kosower, Larsen, Lipstein, Lipatov, Maldacena, Mason, Pennington, Postnikov, Sikorowski, Sever, Spradlin, Trnka, Vergu, Vieira, Volovich and many others • New remarkable representations of gravity amplitudes inspired by twistor string theory. Adamo, Cheung, Hodges, Cachazo, Geyer, Mason, Skinner, etc • Advances in constructing string theory scattering amplitudes with large numbers of external legs. Broedel, Drummond, Green, Mafra, Schlotterer, Stieberger, Taylor, Ragousy, Terasoma, etc • Relations between gravity and gauge theory amplitudes. ZB, Bjerrum-Bohr, Carrasco, Davies, Dennen, O’Connell, Huang, Johansson ,Monteiro, Roiban , etc • NLO QCD multijet processes for LHC physics.
    [Show full text]
  • Classical Field Theories from Hamiltonian Constraint: Local
    Classical field theories from Hamiltonian constraint: Local symmetries and static gauge fields V´aclav Zatloukal∗ Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Bˇrehov´a7, 115 19 Praha 1, Czech Republic and Max Planck Institute for the History of Science, Boltzmannstrasse 22, 14195 Berlin, Germany We consider the Hamiltonian constraint formulation of classical field theories, which treats space- time and the space of fields symmetrically, and utilizes the concept of momentum multivector. The gauge field is introduced to compensate for non-invariance of the Hamiltonian under local trans- formations. It is a position-dependent linear mapping, which couples to the Hamiltonian by acting on the momentum multivector. We investigate symmetries of the ensuing gauged Hamiltonian, and propose a generic form of the gauge field strength. In examples we show how a generic gauge field can be specialized in order to realize gravitational and/or Yang-Mills interaction. Gauge field dynamics is not discussed in this article. Throughout, we employ the mathematical language of geometric algebra and calculus. I. INTRODUCTION The Hamiltonian constraint is a concept useful for Hamiltonian formulation not only of general relativity [1], but, in fact, of a generic field theory, as pointed out in Ref. [2, Ch. 3], and exploited further in [3] and [4]. Characteristic features of this formulation are: finite-dimensional configu- ration space, and multivector-valued momentum variable. In this respect it is congruent with the covariant (or De Donder-Weyl) Hamiltonian formalism [5{13] and should be contrasted with the canonical (or instantaneous) Hamiltonian formalism [14], which utilizes an infinite-dimensional space of field configurations defined at a given instant of time.
    [Show full text]
  • Applications Gauge Theory/Gravity
    APPLICATIONS OF THE GAUGE THEORY/GRAVITY CORRESPONDENCE Andrea Helen Prinsloo A thesis submitted for the degree of Doctor of Philosophy in Applied Mathematics, Department of Mathematics and Applied Mathematics, University of Cape Town. May, 2010 i Abstract The gauge theory/gravity correspondence encompasses a variety of different specific dualities. We study examples of both Super Yang-Mills/type IIB string theory and Super Chern-Simons-matter/type IIA string theory dualities. We focus on the recent ABJM correspondence as an example of the latter. We conduct a detailed investigation into the properties of D-branes and their operator 3 duals. The D2-brane dual giant graviton on AdS4×CP is initially studied: we calculate its spectrum of small fluctuations and consider open string excitations in both the short pp-wave and long semiclassical string limits. We extend Mikhailov's holomorphic curve construction to build a giant graviton on 1;1 AdS5 × T . This is a non-spherical D3-brane configuration, which factorizes at maxi- mal size into two dibaryons on the base manifold T1;1. We present a fluctuation analysis and also consider attaching open strings to the giant's worldvolume. We finally propose 3 an ansatz for the D4-brane giant graviton on AdS4 × CP , which is embedded in the complex projective space. 2 The maximal D4-brane giant factorizes into two CP dibaryons. A comparison is made 2 between the spectrum of small fluctuations about one such CP dibaryon and the conformal dimensions of BPS excitations of the dual determinant operator in ABJM theory. We conclude with a study of the thermal properties of an ensemble of pp-wave strings under a Lunin-Maldacena deformation.
    [Show full text]
  • Quantum Chromodynamics and the Precision Phenomenology of Heavy Quarks
    Quantum Chromodynamics and the Precision Phenomenology of Heavy Quarks Matthew Alexander Lim of Pembroke College This dissertation was submitted to the University of Cambridge for the degree of Doctor of Philosophy in August 2018. ii iii Quantum Chromodynamics and the Precision Phenomenology of Heavy Quarks Matthew Alexander Lim In this thesis we consider the phenomenology of the theory of strong interactions, Quantum Chromodynamics (QCD), with particular reference to the ongoing experimental program at the Large Hadron Collider in CERN. The current progress in precision measurement of Standard Model processes at the LHC experiments must be matched with corresponding precision in theoretical predictions, and to this end we present calculations at next-to-next-to-leading order in perturbation theory of observable quantities involving quarks and gluons, the strongly interacting particles of the SM. Such calculations form the most important class of corrections to observables and are vital if we are to untangle signals of New Physics from LHC data. We consider in particular the amplitudes for five parton interactions at 1- and 2-loop order and present full (in the 1-loop case) and partial (in the 2-loop case) analytic results in terms of rational functions of kinematic invariants multiplying a basis of master integrals. We address the problem of the solution of a system of integration-by-parts identities for Feynman integrals and demonstrate how some current difficulties may be overcome. We consider also the properties of the top quark, and present the NNLO, real-virtual contributions to the calculation of its decay rate. The results are presented as helicity amplitudes so that the full behaviour of the top spin is retained.
    [Show full text]
  • UNIVERSITY of CALIFORNIA Los Angeles the Double Copy: from Scattering to Radiation a Dissertation Submitted in Partial Satisfact
    UNIVERSITY OF CALIFORNIA Los Angeles The Double Copy: From Scattering to Radiation A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Physics by David Alan Chester III 2018 c Copyright by David Alan Chester III 2018 ABSTRACT OF THE DISSERTATION The Double Copy: From Scattering to Radiation by David Alan Chester III Doctor of Philosophy in Physics University of California, Los Angeles, 2018 Professor Zvi Bern, Chair This thesis discusses consequences of color-kinematics duality and applications towards com- puting quantum scattering amplitudes and classical radiation fields. Stemming from this duality, tree-level Bern-Carrasco-Johansson amplitude relations can be extended to one-loop integral coefficient relations for scattering in Yang-Mills theory. The double copy, which also follows from color-kinematics duality, allows for graviton scattering amplitudes to be found from scattering amplitudes in Yang-Mills theory. Additionally, a classical radiative double copy for obtaining gravitational waves in various theories is discussed. As a warm-up, a classical double copy of the Lienard-Wiechert potential in electrodynamics is found within a specific context, which allows for gravitational waves in linearized gravity to be found. Next, radiation in Yang-Mills and Yang-Mills-biadjoint-scalar theories is found, and the radiative double copy of these results allows for radiation in general relativity and Einstein-Yang- Mills theory, repsectively. In light of the recent detection of gravitational waves by the LIGO collaboration, this motivates the search of efficient analytic techniques for computing gravitational radiation. The double copy offers a way to apply methods from particle physics to gravitational-wave astronomy.
    [Show full text]
  • General Relativity Vs. Gauge Theory Gravity
    Experimental Test of Quantum Gravity: General Relativity vs. Gauge Theory Gravity Peter Cameron and Michaele Suisse∗ PO Box 1030 Mattituck, NY USA 11952 (Dated: September 16, 2017) With recent detection of gravitational waves[1, 2], the possibility exists that orientation-dependent detector re- sponses might permit distinguishing between General Relativity (GR) and Gauge Theory Gravity (GTG)[3]. The classical equivalence of these two models was established over twenty years ago.[4{7]. The question is whether this equivalence persists in their respective quantum theories. While such a theory is not yet known to exist for the curved spacetime of GR, the task is not so difficult in the flat Minkowski spacetime of GTG. The language of GTG is geometric Clifford alge- bra, the background-independent[8] interaction lan- guage of fundamental geometric objects of space - Eu- clid's point, line, plane, and volume elements, the ge- ometric objects of Pauli algebra of three-dimensional space. In quantized GTG they are taken to comprise the vacuum wavefunction. Their interactions gener- ate the Dirac algebra of four-dimensional Minkowski spacetime[9]. They permit one to define a geometric wavefunction at the Planck length, and when endowed with experimentally observed quantized electric and FIG. 1. Classical GR says interferometer response is optimal for magnetic fields reveal an exact relation between elec- orientation (A) and less so for (B)[20], whereas quantized GTG tromagnetism and gravity, yielding a naturally finite, is optimal for (B) and less so for (A). confined, and gauge invariant quantum theory that has no free parameters and contains gravity[10{16].
    [Show full text]
  • Applications of the Gauge/Gravity Duality (DRAFT: July 30, 2013)
    Applications of the Gauge/Gravity Duality by Kevin Robert Leslie Whyte B. Applied Science, University of Waterloo, 2004 B. Mathematics, University of Waterloo, 2006 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Doctor of Philosophy in THE FACULTY OF GRADUATE STUDIES (Physics) The University Of British Columbia (Vancouver) August 2013 c Kevin Robert Leslie Whyte, 2013 Abstract While varied applications of gauge/gravity duality have arisen in literature from studies of condensed matter systems including superconductivity to studies of quenched Quantum Chromodynamics (QCD), this thesis focuses on applications of the dual- ity to holographic QCD-like field theories and to inflationary model that uses a QCD-like field theory. In particular the first half of the thesis examines a holographic QCD-like field theory with scalar quarks closely related to the Sakai-Sugimoto model of holo- graphic QCD. The behaviour of baryons and mesons in the model is examined to find a continuous mass spectrum for the mesons, and a baryon that can identified with a topological charge. It then slightly modifies the theory to further study the behaviour of holographic field theories. The second half of the thesis presents a novel model for early Universe infla- tion, using an SU(N) gauge field theory as the inflaton. The inflation model is studied at both weak coupling and strong coupling using the gauge/gravity dual- ity. The robustness of model’s predictions to exciting multiple inflationary fields beyond the single field of its original proposal, and its possible role in breaking the supersymmetry of the Minimal Supersymmetric Standard Model (MSSM) is also explored.
    [Show full text]
  • The Quantum Structure of Space and Time
    QcEntwn Structure &pace and Time This page intentionally left blank Proceedings of the 23rd Solvay Conference on Physics Brussels, Belgium 1 - 3 December 2005 The Quantum Structure of Space and Time EDITORS DAVID GROSS Kavli Institute. University of California. Santa Barbara. USA MARC HENNEAUX Universite Libre de Bruxelles & International Solvay Institutes. Belgium ALEXANDER SEVRIN Vrije Universiteit Brussel & International Solvay Institutes. Belgium \b World Scientific NEW JERSEY LONOON * SINGAPORE BElJlNG * SHANGHAI HONG KONG TAIPEI * CHENNAI Published by World Scientific Publishing Co. Re. Ltd. 5 Toh Tuck Link, Singapore 596224 USA ofJice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK ofice; 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-PublicationData A catalogue record for this hook is available from the British Library. THE QUANTUM STRUCTURE OF SPACE AND TIME Proceedings of the 23rd Solvay Conference on Physics Copyright 0 2007 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereoi may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-256-952-9 ISBN 981-256-953-7 (phk) Printed in Singapore by World Scientific Printers (S) Pte Ltd The International Solvay Institutes Board of Directors Members Mr.
    [Show full text]
  • Gravity, Gauge Theories and Geometric Algebra
    GRAVITY, GAUGE THEORIES AND GEOMETRIC ALGEBRA Anthony Lasenby1, Chris Doran2 and Stephen Gull3 Astrophysics Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 0HE, UK. Abstract A new gauge theory of gravity is presented. The theory is constructed in a flat background spacetime and employs gauge fields to ensure that all relations between physical quantities are independent of the positions and orientations of the matter fields. In this manner all properties of the background spacetime are removed from physics, and what remains are a set of ‘intrinsic’ relations between physical fields. For a wide range of phenomena, including all present experimental tests, the theory repro- duces the predictions of general relativity. Differences do emerge, however, through the first-order nature of the equations and the global properties of the gauge fields, and through the relationship with quantum theory. The properties of the gravitational gauge fields are derived from both classi- cal and quantum viewpoints. Field equations are then derived from an action principle, and consistency with the minimal coupling procedure se- lects an action that is unique up to the possible inclusion of a cosmological constant. This in turn singles out a unique form of spin-torsion interac- tion. A new method for solving the field equations is outlined and applied to the case of a time-dependent, spherically-symmetric perfect fluid. A gauge is found which reduces the physics to a set of essentially Newtonian equations. These equations are then applied to the study of cosmology, and to the formation and properties of black holes. Insistence on find- ing global solutions, together with the first-order nature of the equations, arXiv:gr-qc/0405033v1 6 May 2004 leads to a new understanding of the role played by time reversal.
    [Show full text]