Slides for Chapter 15 Supergravity
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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. -
Report of the Supersymmetry Theory Subgroup
Report of the Supersymmetry Theory Subgroup J. Amundson (Wisconsin), G. Anderson (FNAL), H. Baer (FSU), J. Bagger (Johns Hopkins), R.M. Barnett (LBNL), C.H. Chen (UC Davis), G. Cleaver (OSU), B. Dobrescu (BU), M. Drees (Wisconsin), J.F. Gunion (UC Davis), G.L. Kane (Michigan), B. Kayser (NSF), C. Kolda (IAS), J. Lykken (FNAL), S.P. Martin (Michigan), T. Moroi (LBNL), S. Mrenna (Argonne), M. Nojiri (KEK), D. Pierce (SLAC), X. Tata (Hawaii), S. Thomas (SLAC), J.D. Wells (SLAC), B. Wright (North Carolina), Y. Yamada (Wisconsin) ABSTRACT Spacetime supersymmetry appears to be a fundamental in- gredient of superstring theory. We provide a mini-guide to some of the possible manifesta- tions of weak-scale supersymmetry. For each of six scenarios These motivations say nothing about the scale at which nature we provide might be supersymmetric. Indeed, there are additional motiva- tions for weak-scale supersymmetry. a brief description of the theoretical underpinnings, Incorporation of supersymmetry into the SM leads to a so- the adjustable parameters, lution of the gauge hierarchy problem. Namely, quadratic divergences in loop corrections to the Higgs boson mass a qualitative description of the associated phenomenology at future colliders, will cancel between fermionic and bosonic loops. This mechanism works only if the superpartner particle masses comments on how to simulate each scenario with existing are roughly of order or less than the weak scale. event generators. There exists an experimental hint: the three gauge cou- plings can unify at the Grand Uni®cation scale if there ex- I. INTRODUCTION ist weak-scale supersymmetric particles, with a desert be- The Standard Model (SM) is a theory of spin- 1 matter tween the weak scale and the GUT scale. -
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. -
Off-Shell Interactions for Closed-String Tachyons
Preprint typeset in JHEP style - PAPER VERSION hep-th/0403238 KIAS-P04017 SLAC-PUB-10384 SU-ITP-04-11 TIFR-04-04 Off-Shell Interactions for Closed-String Tachyons Atish Dabholkarb,c,d, Ashik Iqubald and Joris Raeymaekersa aSchool of Physics, Korea Institute for Advanced Study, 207-43, Cheongryangri-Dong, Dongdaemun-Gu, Seoul 130-722, Korea bStanford Linear Accelerator Center, Stanford University, Stanford, CA 94025, USA cInstitute for Theoretical Physics, Department of Physics, Stanford University, Stanford, CA 94305, USA dDepartment of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India E-mail:[email protected], [email protected], [email protected] Abstract: Off-shell interactions for localized closed-string tachyons in C/ZN super- string backgrounds are analyzed and a conjecture for the effective height of the tachyon potential is elaborated. At large N, some of the relevant tachyons are nearly massless and their interactions can be deduced from the S-matrix. The cubic interactions be- tween these tachyons and the massless fields are computed in a closed form using orbifold CFT techniques. The cubic interaction between nearly-massless tachyons with different charges is shown to vanish and thus condensation of one tachyon does not source the others. It is shown that to leading order in N, the quartic contact in- teraction vanishes and the massless exchanges completely account for the four point scattering amplitude. This indicates that it is necessary to go beyond quartic inter- actions or to include other fields to test the conjecture for the height of the tachyon potential. Keywords: closed-string tachyons, orbifolds. -
Introductory Lectures on Quantum Field Theory
Introductory Lectures on Quantum Field Theory a b L. Álvarez-Gaumé ∗ and M.A. Vázquez-Mozo † a CERN, Geneva, Switzerland b Universidad de Salamanca, Salamanca, Spain Abstract In these lectures we present a few topics in quantum field theory in detail. Some of them are conceptual and some more practical. They have been se- lected because they appear frequently in current applications to particle physics and string theory. 1 Introduction These notes are based on lectures delivered by L.A.-G. at the 3rd CERN–Latin-American School of High- Energy Physics, Malargüe, Argentina, 27 February–12 March 2005, at the 5th CERN–Latin-American School of High-Energy Physics, Medellín, Colombia, 15–28 March 2009, and at the 6th CERN–Latin- American School of High-Energy Physics, Natal, Brazil, 23 March–5 April 2011. The audience on all three occasions was composed to a large extent of students in experimental high-energy physics with an important minority of theorists. In nearly ten hours it is quite difficult to give a reasonable introduction to a subject as vast as quantum field theory. For this reason the lectures were intended to provide a review of those parts of the subject to be used later by other lecturers. Although a cursory acquaintance with the subject of quantum field theory is helpful, the only requirement to follow the lectures is a working knowledge of quantum mechanics and special relativity. The guiding principle in choosing the topics presented (apart from serving as introductions to later courses) was to present some basic aspects of the theory that present conceptual subtleties. -
UV Behavior of Half-Maximal Supergravity Theories
UV behavior of half-maximal supergravity theories. Piotr Tourkine, Quantum Gravity in Paris 2013, LPT Orsay In collaboration with Pierre Vanhove, based on 1202.3692, 1208.1255 Understand the pertubative structure of supergravity theories. ● Supergravities are theories of gravity with local supersymmetry. ● Those theories naturally arise in the low energy limit of superstring theory. ● String theory is then a UV completion for those and thus provides a good framework to study their UV behavior. → Maximal and half-maximal supergravities. Maximal supergravity ● Maximally extended supergravity: – Low energy limit of type IIA/B theory, – 32 real supercharges, unique (ungauged) – N=8 in d=4 ● Long standing problem to determine if maximal supergravity can be a consistent theory of quantum gravity in d=4. ● Current consensus on the subject : it is not UV finite, the first divergence could occur at the 7-loop order. ● Impressive progresses made during last 5 years in the field of scattering amplitudes computations. [Bern, Carrasco, Dixon, Dunbar, Johansson, Kosower, Perelstein, Rozowsky etc.] Half-maximal supergravity ● Half-maximal supergravity: – Heterotic string, but also type II strings on orbifolds – 16 real supercharges, – N=4 in d=4 ● Richer structure, and still a lot of SUSY so explicit computations are still possible. ● There are UV divergences in d=4, [Fischler 1979] at one loop for external matter states ● UV divergence in gravity amplitudes ? As we will see the divergence is expected to arise at the four loop order. String models that give half-maximal supergravity “(4,0)” susy “(0,4)” susy ● Type IIA/B string = Superstring ⊗ Superstring Torus compactification : preserves full (4,4) supersymmetry. -
Non-Critical String Theory Formulation of Microtubule Dynamics And
ACT-09/95 CERN-TH.127/95 CTP-TAMU-24/95 ENSLAPP-A|-/95 hep-ph/9505401 Non-Critical String Theory Formulation of Microtubule Dynamics and Quantum Asp ects of Brain Function a; b;c N.E. Mavromatos and D.V. Nanop oulos a Lab oratoire de Physique Theorique ENSLAPP (URA 14-36 du CNRS, asso ciee a l' E.N.S de Lyon, et au LAPP (IN2P3-CNRS) d'Annecy-le-Vieux), Chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux Cedex, France. b Texas A & M University, College Station, TX 77843-424 2, USA and Astroparticle Physics Group, Houston Advanced Research Center (HARC), The Mitchell Campus, Wo o dlands, TX 77381, USA. c CERN, Theory Division, Geneva 23 Switzerland Abstract Microtubule (MT) networks, subneural paracrystalline cytosceletal structures, seem to play a fundamental role in the neurons. We cast here the complicated MT dynamics in processed by the SLAC/DESY Libraries on 30 May 1995. 〉 the form of a 1 + 1-dimensional non-critical string theory,thus enabling us to provide a consistent quantum treatment of MTs, including enviromental friction e ects. We suggest, thus, that the MTs are the microsites, in the brain, for the emergence of stable, macroscopic PostScript quantum coherent states, identi able with the preconscious states. Quantum space-time e ects, as describ ed by non-critical string theory, trigger then an organizedcol lapse of the coherent states down to a sp eci c or conscious state. The whole pro cess we estimate to take O (1 sec), in excellent agreement with a plethora of exp erimental/observational ndings. -
Gravitino Dark Matter
GRAVITINO DARK MATTER Wilfried Buchm¨uller DESY, Hamburg LAUNCH09, Nov. 2009, MPK Heidelberg Why Gravitino Dark Matter? Supergravity predicts the gravitino, analog of W and Z bosons in electroweak theory; may be LSP, natural DM candidate: m < 1keV, hot DM, (Pagels, Primack ’81) • 3/2 1keV < m3/2 < 15keV, warm DM, (Gorbunov, Khmelnitsky, Rubakov ’08) • ∼ ∼ 100keV < m < 10MeV, cold DM, gauge mediation and thermal • 3/2 leptogenesis∼ (Fuji, Ibe,∼ Yanagida ’03); recently proven to be correct by F-theory (Heckman, Tavanfar, Vafa ’08) 10GeV < m < 1TeV, cold DM, gaugino/gravity mediation and • 3/2 thermal leptogenesis∼ ∼ (Bolz, WB, Pl¨umacher ’98) Baryogenesis, (gravitino) DM and primordial nucleosynthesis (BBN) strongly correlated in cosmological history. 1 Gravitino Problem Thermally produced gravitino number density grows with reheating temperature after inflation (Khlopov, Linde ’83; Ellis, Kim, Nanopoulos ’84;...), n3/2 α3 2 TR. nγ ∝ Mp For unstable gravitinos, nucleosynthesis implies stringent upper bound on reheating temperature TR (Kawasaki, Kohri, Moroi ’05; ...), T < (1) 105 GeV, R O × hence standard mSUGRA with neutralino LSP incompatible with baryogenesis via thermal leptogenesis where T 1010 GeV !! R ∼ Possible way out: Gravitino LSP, explains dark matter! 2 Gravitino Virtue Can one understand the amount of dark matter, ΩDM 0.23, with Ω = ρ /ρ , if gravitinos are dominant component, i.e. Ω≃ Ω ? DM DM c DM ≃ 3/2 Production mechanisms: (i) WIMP decays, i.e., ‘Super-WIMPs’ (Covi, Kim, Roszkowski ’99; Feng, Rajaraman, Takayama ’03), m3/2 Ω3/2 = ΩNLSP , mNLSP independent of initial temperature TR (!), but inconsistent with BBN constraints; (ii) Thermal production, from 2 2 QCD processes, → 2 TR 100GeV mg˜(µ) Ω3/2h 0.5 10 . -
Solutions and Democratic Formulation of Supergravity Theories in Four Dimensions
Universidad Consejo Superior Aut´onoma de Madrid de Investigaciones Cient´ıficas Facultad de Ciencias Instituto de F´ısica Te´orica Departamento de F´ısica Te´orica IFT–UAM/CSIC Solutions and Democratic Formulation of Supergravity Theories in Four Dimensions Mechthild Hubscher¨ Madrid, May 2009 Copyright c 2009 Mechthild Hubscher.¨ Universidad Consejo Superior Aut´onoma de Madrid de Investigaciones Cient´ıficas Facultad de Ciencias Instituto de F´ısica Te´orica Departamento de F´ısica Te´orica IFT–UAM/CSIC Soluciones y Formulaci´on Democr´atica de Teor´ıas de Supergravedad en Cuatro Dimensiones Memoria de Tesis Doctoral realizada por Da Mechthild Hubscher,¨ presentada ante el Departamento de F´ısica Te´orica de la Universidad Aut´onoma de Madrid para la obtenci´on del t´ıtulo de Doctora en Ciencias. Tesis Doctoral dirigida por Dr. D. Tom´as Ort´ın Miguel, Investigador Cient´ıfico del Consejo Superior de Investigaciones Cient´ıficas, y Dr. D. Patrick Meessen, Investigador Contratado por el Consejo Superior de Investigaciones Cient´ıficas. Madrid, Mayo de 2009 Contents 1 Introduction 1 1.1 Supersymmetry, Supergravity and Superstring Theory . ....... 1 1.2 Gauged Supergravity and the p-formhierarchy . 10 1.3 Supersymmetric configurations and solutions of Supergravity ..... 18 1.4 Outlineofthisthesis............................ 23 2 Ungauged N =1, 2 Supergravity in four dimensions 25 2.1 Ungauged matter coupled N =1Supergravity. 25 2.1.1 Perturbative symmetries of the ungauged theory . ... 27 2.1.2 Non-perturbative symmetries of the ungauged theory . ..... 33 2.2 Ungauged matter coupled N =2Supergravity. 35 2.2.1 N = 2, d =4SupergravityfromStringTheory . 42 3 Gauging Supergravity and the four-dimensional tensor hierarchy 49 3.1 Theembeddingtensorformalism . -
Super-Higgs in Superspace
Article Super-Higgs in Superspace Gianni Tallarita 1,* and Moritz McGarrie 2 1 Departamento de Ciencias, Facultad de Artes Liberales, Universidad Adolfo Ibáñez, Santiago 7941169, Chile 2 Deutsches Elektronen-Synchrotron, DESY, Notkestrasse 85, 22607 Hamburg, Germany; [email protected] * Correspondence: [email protected] or [email protected] Received: 1 April 2019; Accepted: 10 June 2019; Published: 14 June 2019 Abstract: We determine the effective gravitational couplings in superspace whose components reproduce the supergravity Higgs effect for the constrained Goldstino multiplet. It reproduces the known Gravitino sector while constraining the off-shell completion. We show that these couplings arise by computing them as quantum corrections. This may be useful for phenomenological studies and model-building. We give an example of its application to multiple Goldstini. Keywords: supersymmetry; Goldstino; superspace 1. Introduction The spontaneous breakdown of global supersymmetry generates a massless Goldstino [1,2], which is well described by the Akulov-Volkov (A-V) effective action [3]. When supersymmetry is made local, the Gravitino “eats” the Goldstino of the A-V action to become massive: The super-Higgs mechanism [4,5]. In terms of superfields, the constrained Goldstino multiplet FNL [6–12] is equivalent to the A-V formulation (see also [13–17]). It is, therefore, natural to extend the description of supergravity with this multiplet, in superspace, to one that can reproduce the super-Higgs mechanism. In this paper we address two issues—first we demonstrate how the Gravitino, Goldstino, and multiple Goldstini obtain a mass. Secondly, by using the Spurion analysis, we write down the most minimal set of new terms in superspace that incorporate both supergravity and the Goldstino multiplet in order to reproduce the super-Higgs mechanism of [5,18] at lowest order in M¯ Pl. -
Andrew Thomson Dissertation.Pdf
PHENOMENOLOGY OF COMPACTIFICATIONS OF M-THEORY ON MANIFOLDS OF G2 HOLONOMY by Andrew James Thomson Supervisor: Kelly Stelle A dissertation submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London 24 September 2010 Contents I. Introduction 3 II. Holonomy and G2 manifolds 7 III. Chirality and singular manifolds 11 IV. Moduli stabilization and the hierarchy problem 14 V. Conclusion 17 References 19 2 I. Introduction The Standard Model is a phenomenally successful theory of particle physics, well tested at quantum mechanical level up to the TeV energy scale, and renormalizable (notwithstanding that the Higgs particle has not been observed yet) [1]. However there are several issues (or at least perceived ones) with the model. First of all, it only describes three of the four fundamental forces (the strong, electromagnetic and weak forces) in a quantum manner, leaving gravity still described only in a classical fashion; however we will not be concerned with this any further during this dissertation. The primary issue with which we will be concerned is the so-called hierarchy problem (also known as the weak-scale instability) – why there are two (electroweak and Planck) mass scales and why they are so far apart, why the electroweak scale is not modified at loop level by the Planck scale and whether there are any other scales between them. [1,2] One wonders why we should be concerned with as yet purely theoretical imperfections which have not yet manifested themselves in any experimental observations. One only has to look to the history of the standard model itself for a precedent for looking for physics beyond it – the earliest theories of the weak interaction, which were based on the interaction of four fermions at a point, broke down when calculated to higher order at the then unimaginably high energies of 300 GeV (Heisenberg 1939) before they had been violated by any observation. -
TASI 2008 Lectures: Introduction to Supersymmetry And
TASI 2008 Lectures: Introduction to Supersymmetry and Supersymmetry Breaking Yuri Shirman Department of Physics and Astronomy University of California, Irvine, CA 92697. [email protected] Abstract These lectures, presented at TASI 08 school, provide an introduction to supersymmetry and supersymmetry breaking. We present basic formalism of supersymmetry, super- symmetric non-renormalization theorems, and summarize non-perturbative dynamics of supersymmetric QCD. We then turn to discussion of tree level, non-perturbative, and metastable supersymmetry breaking. We introduce Minimal Supersymmetric Standard Model and discuss soft parameters in the Lagrangian. Finally we discuss several mech- anisms for communicating the supersymmetry breaking between the hidden and visible sectors. arXiv:0907.0039v1 [hep-ph] 1 Jul 2009 Contents 1 Introduction 2 1.1 Motivation..................................... 2 1.2 Weylfermions................................... 4 1.3 Afirstlookatsupersymmetry . .. 5 2 Constructing supersymmetric Lagrangians 6 2.1 Wess-ZuminoModel ............................... 6 2.2 Superfieldformalism .............................. 8 2.3 VectorSuperfield ................................. 12 2.4 Supersymmetric U(1)gaugetheory ....................... 13 2.5 Non-abeliangaugetheory . .. 15 3 Non-renormalization theorems 16 3.1 R-symmetry.................................... 17 3.2 Superpotentialterms . .. .. .. 17 3.3 Gaugecouplingrenormalization . ..... 19 3.4 D-termrenormalization. ... 20 4 Non-perturbative dynamics in SUSY QCD 20 4.1 Affleck-Dine-Seiberg