String Solitons
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Nonextremal Black Holes, Subtracted Geometry and Holography
Nonextremal Black Holes, Subtracted Geometry and Holography Mirjam Cvetič Einstein’s theory of gravity predicts Black Holes Due to it’s high mass density the space-time curved so much that objects traveling toward it reach a point of no return à Horizon (& eventually reaches space-time singularity) Black holes `behave’ as thermodynamic objects w/ Bekenstein-Hawking entropy: S=¼ Ahorizon Ahorizon= area of the black hole horizon (w/ ħ=c=GN=1) Horizon-point of no return Space-time singularity Key Issue in Black Hole Physics: How to relate Bekenstein-Hawking - thermodynamic entropy: Sthermo=¼ Ahor (Ahor= area of the black hole horizon; c=ħ=1;GN=1) to Statistical entropy: Sstat = log Ni ? Where do black hole microscopic degrees Ni come from? Horizon Space-time singularity Black Holes in String Theory The role of D-branes D(irichlet)-branes Polchinski’96 boundaries of open strings with charges at their ends closed strings I. Implications for particle physics (charged excitations)-no time II. Implications for Black Holes Dual D-brane interpretation: extended massive gravitational objects D-branes in four-dimensions: part of their world-volume on compactified space & part in internal compactified space Cartoon of (toroidal) compactification; D-branes as gravitational objects Thermodynamic BH Entropy & wrap cycles in internal space: Statistical field theory interpretation intersecting D-branes in compact dimensions & charged black holes in four dim. space-time (w/ each D-brane sourcing charge Q ) i D-branes as a boundary of strings: microscopic degrees Ni are string excitations on intersecting D-branes w/ S = log Ni Strominger & Vafa ’96 the same! Prototype: four-charge black hole w/ S= π√Q1Q2P3P4 M.C. -
Supergravity and Its Legacy Prelude and the Play
Supergravity and its Legacy Prelude and the Play Sergio FERRARA (CERN – LNF INFN) Celebrating Supegravity at 40 CERN, June 24 2016 S. Ferrara - CERN, 2016 1 Supergravity as carved on the Iconic Wall at the «Simons Center for Geometry and Physics», Stony Brook S. Ferrara - CERN, 2016 2 Prelude S. Ferrara - CERN, 2016 3 In the early 1970s I was a staff member at the Frascati National Laboratories of CNEN (then the National Nuclear Energy Agency), and with my colleagues Aurelio Grillo and Giorgio Parisi we were investigating, under the leadership of Raoul Gatto (later Professor at the University of Geneva) the consequences of the application of “Conformal Invariance” to Quantum Field Theory (QFT), stimulated by the ongoing Experiments at SLAC where an unexpected Bjorken Scaling was observed in inclusive electron- proton Cross sections, which was suggesting a larger space-time symmetry in processes dominated by short distance physics. In parallel with Alexander Polyakov, at the time in the Soviet Union, we formulated in those days Conformal invariant Operator Product Expansions (OPE) and proposed the “Conformal Bootstrap” as a non-perturbative approach to QFT. S. Ferrara - CERN, 2016 4 Conformal Invariance, OPEs and Conformal Bootstrap has become again a fashionable subject in recent times, because of the introduction of efficient new methods to solve the “Bootstrap Equations” (Riccardo Rattazzi, Slava Rychkov, Erik Tonni, Alessandro Vichi), and mostly because of their role in the AdS/CFT correspondence. The latter, pioneered by Juan Maldacena, Edward Witten, Steve Gubser, Igor Klebanov and Polyakov, can be regarded, to some extent, as one of the great legacies of higher dimensional Supergravity. -
Band Spectrum Is D-Brane
Prog. Theor. Exp. Phys. 2016, 013B04 (26 pages) DOI: 10.1093/ptep/ptv181 Band spectrum is D-brane Koji Hashimoto1,∗ and Taro Kimura2,∗ 1Department of Physics, Osaka University, Toyonaka, Osaka 560-0043, Japan 2Department of Physics, Keio University, Kanagawa 223-8521, Japan ∗E-mail: [email protected], [email protected] Received October 19, 2015; Revised November 13, 2015; Accepted November 29, 2015; Published January 24 , 2016 Downloaded from ............................................................................... We show that band spectrum of topological insulators can be identified as the shape of D-branes in string theory. The identification is based on a relation between the Berry connection associated with the band structure and the Atiyah–Drinfeld–Hitchin–Manin/Nahm construction of solitons http://ptep.oxfordjournals.org/ whose geometric realization is available with D-branes. We also show that chiral and helical edge states are identified as D-branes representing a noncommutative monopole. ............................................................................... Subject Index B23, B35 1. Introduction at CERN - European Organization for Nuclear Research on July 8, 2016 Topological insulators and superconductors are one of the most interesting materials in which theo- retical and experimental progress have been intertwined each other. In particular, the classification of topological phases [1,2] provided concrete and rigorous argument on stability and the possibility of topological insulators and superconductors. The key to finding the topological materials is their electron band structure. The existence of gapless edge states appearing at spatial boundaries of the material signals the topological property. Identification of possible electron band structures is directly related to the topological nature of topological insulators. It is important, among many possible appli- cations of topological insulators, to gain insight into what kind of electron band structure is possible for topological insulators with fixed topological charges. -
String Theory in Magnetic Monopole Backgrounds
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server EFI-98-58, ILL-(TH)-98-06 hep-th/9812027 String Theory in Magnetic Monopole Backgrounds David Kutasov1,FinnLarsen1, and Robert G. Leigh2 1Enrico Fermi Institute, University of Chicago, 5640 S. Ellis Av., Chicago, IL 60637 2Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801 We discuss string propagation in the near-horizon geometry generated by Neveu-Schwarz fivebranes, Kaluza-Klein monopoles and fundamental strings. When the fivebranes and KK monopoles are wrapped around a compact four-manifold , the geometry is AdS S3/ZZ and the M 3 × N ×M spacetime dynamics is expected to correspond to a local two dimensional conformal field theory. We determine the moduli space of spacetime CFT’s, study the spectrum of the theory and compare the chiral primary operators obtained in string theory to supergravity expectations. 12/98 1. Introduction It is currently believed that many (perhaps all) vacua of string theory have the prop- erty that their spacetime dynamics can be alternatively described by a theory without gravity [1,2,3,4]. This theory is in general non-local, but in certain special cases it is ex- pected to become a local quantum field theory (QFT). It is surprising that string dynamics can be equivalent to a local QFT. A better understanding of this equivalence would have numerous applications to strongly coupled gauge theory, black hole physics and a non- perturbative formulation of string theory. An important class of examples for which string dynamics is described by local QFT is string propagation on manifolds that include an anti-de-Sitter spacetime AdSp+1[3,5,6]. -
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. -
Arxiv:Hep-Th/0006117V1 16 Jun 2000 Oadmarolf Donald VERSION HYPER - Style
Preprint typeset in JHEP style. - HYPER VERSION SUGP-00/6-1 hep-th/0006117 Chern-Simons terms and the Three Notions of Charge Donald Marolf Physics Department, Syracuse University, Syracuse, New York 13244 Abstract: In theories with Chern-Simons terms or modified Bianchi identities, it is useful to define three notions of either electric or magnetic charge associated with a given gauge field. A language for discussing these charges is introduced and the proper- ties of each charge are described. ‘Brane source charge’ is gauge invariant and localized but not conserved or quantized, ‘Maxwell charge’ is gauge invariant and conserved but not localized or quantized, while ‘Page charge’ conserved, localized, and quantized but not gauge invariant. This provides a further perspective on the issue of charge quanti- zation recently raised by Bachas, Douglas, and Schweigert. For the Proceedings of the E.S. Fradkin Memorial Conference. Keywords: Supergravity, p–branes, D-branes. arXiv:hep-th/0006117v1 16 Jun 2000 Contents 1. Introduction 1 2. Brane Source Charge and Brane-ending effects 3 3. Maxwell Charge and Asymptotic Conditions 6 4. Page Charge and Kaluza-Klein reduction 7 5. Discussion 9 1. Introduction One of the intriguing properties of supergravity theories is the presence of Abelian Chern-Simons terms and their duals, the modified Bianchi identities, in the dynamics of the gauge fields. Such cases have the unusual feature that the equations of motion for the gauge field are non-linear in the gauge fields even though the associated gauge groups are Abelian. For example, massless type IIA supergravity contains a relation of the form dF˜4 + F2 H3 =0, (1.1) ∧ where F˜4, F2,H3 are gauge invariant field strengths of rank 4, 2, 3 respectively. -
Two-Dimensional Instantons with Bosonization and Physics of Adjoint QCD2
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Preprint ITEP–TH–21/96 Two-Dimensional Instantons with Bosonization and Physics of Adjoint QCD2. A.V. Smilga ITEP, B. Cheremushkinskaya 25, Moscow 117259, Russia Abstract We evaluate partition functions ZI in topologically nontrivial (instanton) gauge sectors in the bosonized version of the Schwinger model and in a gauged WZNW model corresponding to QCD2 with adjoint fermions. We show that the bosonized model is equivalent to the fermion model only if a particular form of the WZNW action with gauge-invariant integrand is chosen. For the exact correspondence, it is necessary to 2 integrate over the ways the gauge group SU(N)/ZN is embedded into the full O(N −1) group for the bosonized matter field. For even N, one should also take into account the 2 n contributions of both disconnected components in O(N − 1). In that case, ZI ∝ m 0 for small fermion masses where 2n0 coincides with the number of fermion zero modes in n a particular instanton background. The Taylor expansion of ZI /m 0 in mass involves only even powers of m as it should. The physics of adjoint QCD2 is discussed. We argue that, for odd N, the discrete chiral symmetry Z2 ⊗Z2 present in the action is broken spontaneously down to Z2 and the fermion condensate < λλ¯ >0 is formed. The system undergoes a first order phase transition at Tc = 0 so that the condensate is zero at an arbitrary small temperature. -
Supersymmetric Sigma Models with Torsion
R/95/15 May, 1995 Elliptic monop oles and (4,0)-sup ersymmetric sigma mo dels with torsion G. Papadopoulos D.A.M.T.P University of Cambridge Silver Street Cambridge CB3 9EW ABSTRACT We explicitly construct the metric and torsion couplings of two-dimensional processed by the SLAC/DESY Libraries on 21 May 1995. 〉 (4,0)-sup ersymmetric sigma mo dels with target space a four-manifold that are invariant under a U (1) symmetry generated by a tri-holomorphic Killing vector eld PostScript that leaves in addition the torsion invariant. We show that the metric couplings arise from magnetic monop oles on the three-sphere which is the space of orbits of the group action generated by the tri-holomorphic Killing vector eld on the sigma mo del target manifold. We also examine the global structure of a sub class of these metrics that are in addition SO(3)-invariant and nd that the only non-singular one, for mo dels with non-zero torsion, is that of SU (2) U (1) WZW mo del. HEP-TH-9505119 1. Intro duction It has b een known for sometime that there is an interplaybetween the num- b er of sup ersymmetries which leave the action of a sigma mo del invariant and the geometry of its target space. More recently, sigma mo dels with symmetries gener- ated by Killing vector elds are a fertile area for investigation of the prop erties of T-duality. The couplings of two-dimensional sigma mo dels are the metric g and a lo cally de ned two-form b on the sigma mo del manifold M. -
Five-Branes in Heterotic Brane-World Theories
SUSX-TH/01-037 HUB-EP-01/34 hep-th/0109173 Five-Branes in Heterotic Brane-World Theories Matthias Br¨andle1∗ and Andr´eLukas2§ 1Institut f¨ur Physik, Humboldt Universit¨at Invalidenstraße 110, 10115 Berlin, Germany 2Centre for Theoretical Physics, University of Sussex Falmer, Brighton BN1 9QJ, UK Abstract The effective action for five-dimensional heterotic M-theory in the presence of five-branes is systemat- ically derived from Hoˇrava-Witten theory coupled to an M5-brane world-volume theory. This leads to a 1 five-dimensional N = 1 gauged supergravity theory on S /Z2 coupled to four-dimensional N = 1 theories residing on the two orbifold fixed planes and an additional bulk three-brane. We analyse the properties of this action, particularly the four-dimensional effective theory associated with the domain-wall vacuum state. arXiv:hep-th/0109173v2 8 Oct 2001 The moduli K¨ahler potential and the gauge-kinetic functions are determined along with the explicit relations between four-dimensional superfields and five-dimensional component fields. ∗email: [email protected] §email: [email protected] 1 Introduction A large class of attractive five-dimensional brane-world models can be constructed by reducing Hoˇrava-Witten theory [1, 2, 3] on Calabi-Yau three-folds. This procedure has been first carried out in Ref. [4, 5, 6] and it leads 1 to gauged five-dimensional N = 1 supergravity on the orbifold S /Z2 coupled to N = 1 gauge and gauge matter multiplets located on the two four-dimensional orbifold fixed planes. It has been shown [7]–[13] that a phenomeno- logically interesting particle spectrum on the orbifold planes can be obtained by appropriate compactifications. -
Flux Tubes, Domain Walls and Orientifold Planar Equivalence
Flux tubes, domain walls and orientifold planar equivalence Agostino Patella CERN GGI, 5 May 2011 Agostino Patella (CERN) Tubes and walls GGI, 5/5/11 1 / 19 Introduction Orientifold planar equivalence Orientifold planar equivalence OrQCD 2 SU(N) gauge theory (λ = g N fixed) with Nf Dirac fermions in the antisymmetric representation is equivalent in the large-N limit and in a common sector to AdQCD 2 SU(N) gauge theory (λ = g N fixed) with Nf Majorana fermions in the adjoint representation if and only if C-symmetry is not spontaneously broken. Agostino Patella (CERN) Tubes and walls GGI, 5/5/11 2 / 19 2 Z Z ff e−N W(J) = DADψDψ¯ exp −S(A, ψ, ψ¯) + N2 J(x)O(x)d4x Introduction Orientifold planar equivalence Gauge-invariant common sector AdQCD BOSONIC C-EVEN FERMIONIC C-EVEN BOSONIC C-ODD FERMIONIC C-ODD ~ w OrQCD BOSONIC C-EVEN BOSONIC C-ODD COMMON SECTOR Agostino Patella (CERN) Tubes and walls GGI, 5/5/11 3 / 19 Introduction Orientifold planar equivalence Gauge-invariant common sector AdQCD BOSONIC C-EVEN FERMIONIC C-EVEN BOSONIC C-ODD FERMIONIC C-ODD ~ w OrQCD BOSONIC C-EVEN BOSONIC C-ODD COMMON SECTOR 2 Z Z ff e−N W(J) = DADψDψ¯ exp −S(A, ψ, ψ¯) + N2 J(x)O(x)d4x lim WOr(J) = lim WAd(J) N→∞ N→∞ Agostino Patella (CERN) Tubes and walls GGI, 5/5/11 3 / 19 Introduction Orientifold planar equivalence Gauge-invariant common sector AdQCD BOSONIC C-EVEN FERMIONIC C-EVEN BOSONIC C-ODD FERMIONIC C-ODD ~ w OrQCD BOSONIC C-EVEN BOSONIC C-ODD COMMON SECTOR 2 Z Z ff e−N W(J) = DADψDψ¯ exp −S(A, ψ, ψ¯) + N2 J(x)O(x)d4x hO(x ) ··· O(xn)i hO(x ) ··· -
Dirac Equation for Strings in Minkowski Space-Time and Then Study the Radial Vibrations of the String
Dirac equation for strings Maciej Trzetrzelewski ∗ M. Smoluchowski Institute of Physics, Jagiellonian University, Lojasiewicza, St. 11, 30-348 Krak´ow, Poland Abstract Starting with a Nambu-Goto action, a Dirac-like equation can be constructed by taking the square-root of the momentum constraint. The eigenvalues of the resulting Hamiltonian are real and correspond to masses of the excited string. In particular there are no tachyons. A special case of radial oscillations of a closed string in Minkowski space-time admits exact solutions in terms of wave functions of the harmonic oscillator. 1 Introduction In 1962 Dirac considered the possibility that leptons may be described arXiv:1302.5907v3 [hep-th] 14 Feb 2018 by extended objects of spherical topology [1, 2]. In this way one could understand the muon as an excitation of the ground state of the membrane - the electron. Anticipating Nambu [3] and Goto [4] by almost a decade he introduced what is now known as a generalization of the Nambu-Goto action to the case of membranes. Using Bohr- Sommerfeld approximation for the Hamiltonian corresponding to the radial mode, one can then show [1] that the mass of the first excitation is about 53me where me is the mass of the electron. This is about a quarter of the observed mass of the muon. In fact, when instead of ∗e-mail: [email protected] 1 the Bohr-Sommerfeld approximation one uses, more precise, numeri- cal methods one finds that the correct value of the first excitation is about 43me [5, 6]. Therefore Dirac’s model ”explains” 1/5th of the actual value of the muon mass. -
Supersymmetry and Stationary Solutions in Dilaton-Axion Gravity" (1994)
University of Massachusetts Amherst ScholarWorks@UMass Amherst Physics Department Faculty Publication Series Physics 1994 Supersymmetry and stationary solutions in dilaton- axion gravity R Kallosh David Kastor University of Massachusetts - Amherst, [email protected] T Ortín T Torma Follow this and additional works at: https://scholarworks.umass.edu/physics_faculty_pubs Part of the Physical Sciences and Mathematics Commons Recommended Citation Kallosh, R; Kastor, David; Ortín, T; and Torma, T, "Supersymmetry and stationary solutions in dilaton-axion gravity" (1994). Physics Review D. 1219. Retrieved from https://scholarworks.umass.edu/physics_faculty_pubs/1219 This Article is brought to you for free and open access by the Physics at ScholarWorks@UMass Amherst. It has been accepted for inclusion in Physics Department Faculty Publication Series by an authorized administrator of ScholarWorks@UMass Amherst. For more information, please contact [email protected]. SU-ITP-94-12 UMHEP-407 QMW-PH-94-12 hep-th/9406059 SUPERSYMMETRY AND STATIONARY SOLUTIONS IN DILATON-AXION GRAVITY Renata Kallosha1, David Kastorb2, Tom´as Ort´ınc3 and Tibor Tormab4 aPhysics Department, Stanford University, Stanford CA 94305, USA bDepartment of Physics and Astronomy, University of Massachusetts, Amherst MA 01003 cDepartment of Physics, Queen Mary and Westfield College, Mile End Road, London E1 4NS, U.K. ABSTRACT New stationary solutions of 4-dimensional dilaton-axion gravity are presented, which correspond to the charged Taub-NUT and Israel-Wilson-Perj´es (IWP) solu- tions of Einstein-Maxwell theory. The charged axion-dilaton Taub-NUT solutions are shown to have a number of interesting properties: i) manifest SL(2, R) sym- arXiv:hep-th/9406059v1 10 Jun 1994 metry, ii) an infinite throat in an extremal limit, iii) the throat limit coincides with an exact CFT construction.