Monopoles and Skyrmions. Ya. Shnir. Quarks-2010
|
|
- Conrad Kennedy
- 6 years ago
- Views:
Transcription
1 Monopoles and Skyrmions Ya. Shnir Quarks-2010 Коломна, Россия, 8 Июня 2010
2 Outline Abelian and non-abelian magnetic monopoles BPS monopoles Rational maps and construction of multimonopoles SU(2) axially symmetric multimonopoles Monopole-antimonopole chains Multimonopole moduli space Skyrmions Skyrme model Construction of multiskyrmions Axially symmetric multiskyrmions Rational maps and multiskyrmions Skyrmion-antiSkyrmion chains Multiskyrmions moduli space Summary and outlook
3 Yang-Mills Mills-Higgs Theory S= 1 2 d 4 x{f µν F µν + (D µ Φ)(D µ Φ) V(Φ)} F µν = µ A ν ν A µ +ie[a µ,a ν ] D µ Φ= µ Φ+ie[A µ,φ] V(Φ)=λ(Φ 2 η 2 ) 2 t Hooft-Polyakov static spherically symmetric solution φ a = ra er 2 H(eηr); A a n =ε amn rm er 2 (1 K(eηr)) R c ~m v -1
4 Bogomolny equations: BPS monopole mass: BPS monopoles λ =0, B k = D k F M = 4ph/ e Homotopy group π 2 (S 2 ) Long-range scalar field F ~ 1/r No net interaction between the BPS monopoles Analytical solution of the BPS equations: K= ξ sinhξ ; H=ξcothξ 1 Magnetic charge of a monopole is a topological number Φ: S 2 S 2 Sir M. Atiyah,, R. Ward (1977), P. Forgacs et al (1981), W. Nahm (1982), P. Sutcliffe (1996) and other
5 Self-dual monopoles vs non-self dual monopoles BPS monopoles: In the limit h=0 the energy becomes: E=Tr d 3 x { 1 4 (ε ijkf ij ±D i Φ) ε ijkf ij D k Φ } The first order Bogomol'nyi equations yield absolute minimum: M =4πg B k =±D k Φ No net interaction between the BPS monopoles: the electromagnetic repulsion is compensated by the long-range scalar interaction. Non self-dual monopoles: They are solutions of the second order Yang-Mills equations: µ F µν =0 E>M BPS even if g=0 (deformations of the topologically trivial sector) The constituents are non BPS monopoles and/or vortices in a static equilibrium; separation is relatively small, there are no long-range forces
6 Rational map monopoles There is a transformation of a monopole into a rational map from the Riemanian sphere to inself: R: S 2 # S 2 (P. Sutcliffe, N.Manton et al) R(z)= a(z) b(z) = a 1z n 1 + +a n z n +b 1 z n 1 + +b n, z=x 1 +ix 2 Construction of the rational maps monopoles: Represent BPS equation in spherical coordinates r,z,z Impose a complex gauge Φ= ia r = i 2 U 1 r U, A z =U 1 z U, A z =0 Construct the monopoles using { U exp 2r 1+ R 2 ( R 2 1 2R 2R 1 R 2 )}
7 R = 1/z: one spherically symmetric monopole centered at the origin; R(z) = a 1z+a 2 z 2 +b 1 z+b 2 : two monopoles R(z)= i 3z 2 1 z(z 2 i : Tetrahedral monopoles (degree 3 map) 3) R(z)= z4 +2i 3z 2 +1 z 4 2iz 2 : Octahedral monopoles (degree 4 map) 3+1
8 Numerical Technique Energy minimization approach (static solutions in 2d and in 3d) supercomputers and grid systems Solution of system of PDE s obtained by imposing some symmetry conditions, boundary problem in in 2d and in 3d: Newton-Raphson iterative procedure (FIDISOL/CADSOL package); boundary problem in d1 (COLSYS package) Gradient flow method Dynamics of the solitons: : (pseudo( pseudo) spectral methods, symplectic methods.
9 Non-BPS axially symmetric monopoles MA pair: magnetic dipole (Taubes, Nahm, Rüber, R Kleihaus,Kunz & Shnir) A µ dx µ = ( K 1 r dr+(1 K 2)dθ ) τ (n) ϕ 2e nsinθ ( ) Φ=Φ aτa 2 = τ r H (n,m) τ 1 2 +H (n,m) θ 2 2. ( ) τ K (n,m) r 3 2e +(1 K 4 ) τ(n,m) θ 2e dϕ; Magnetic charge: Q= 1 2π S 2 (ΦdΦ dφ) = 1 2 n[1 ( 1)m ]
10 Monopole-antimonopole chains
11 Effective electromagnetic interaction } `t Hooft tensor: F µν ={ˆΦF µν 2eˆΦD i µˆφd νˆφ The electric and magnetic (topological) currents: µ F µν =4πjν; el µ F µν =4πjν mag The magnetic field if generated by the magnetic charges and electric currents j el r =jel θ =0; 4πjel ϕ = 2 1 ra ϕ +sinθ θ r 2 sinθ θa ϕ
12 Effective electromagnetic interaction `t Hooft tensor: ˆ Fµν Fµν = Φ Φ i ˆ ˆ Dν Φ ˆ Φ Dµ Φ Φ Φ 2e Φ The electric and magnetic (topological) currents: µ Fµν = 4π jνel ; µ F µν = 4π jνmag The magnetic field if generated by the magnetic charges and electric currents jrel = jθel = 0; 4πjϕel = r2 Aϕ + sin θ θ r2 s1in θ θ Aϕ
13 Skyrme field L= d 3 x Skyrmions U SU(2); R µ =( µ U)U 1 { } F 2 π 16 Tr(R µr µ ) 1 32e Tr([R 2 µ,r ν ][R µ,r ν ])+ m2 π F2 π 8 Tr(1 U) Nonlinear pion theory: U =φ 0 +iσ k φ k, φ 2 0 +φ2 k =1 Baryon charge is identified with the topological number U : S 3 S 3 B= 1 24π 2 d 3 xε ijk Tr(R i R j R k ) Homotopy group π 3 (S 3 ) B= 1: Spherically symmetric skyrmion U =exp{if(r)ˆn σ} ˆn=(sinθcosϕ,sinθsinϕ,cosθ) Boundary conditions: f ( r), with f (0) = πk, and The approximation : f ( ) = 0. f ( r) = 4 arctan[exp(r) ]
14 Skyrmion s interaction There is no self-dual skyrmions: E í B A single Skyrmion is approximated by a triplet of orthogonal dipoles Field equations: Asymptotically The dipole-dipole interaction energy Attractive channel: ( µ R µ [Rν,[R ν R µ ]] ) =0 φ k d k r k 4πr 3 +O(r 3 ); φ 0 1 R ñn There are 6 zero modes of the B=1 Skyrmion: 3 translations + 3 rotations E int = 2d2 3πR 3 (cosα 1)[1 3( R n)] Translations: U iu 1 2( k U)U U 1 2 ( d 3 xtr( i U i U ) 1 2 Rotations (Adkins, Nappi & Witten (1983)); rigid body approximation U A(t)UA(t)
15 Axially symmetric multiskyrmions Trigonometric parametrisation: φ α =sinfsingn α ; φ 3 =sinfcosg; φ 4 =cosf; n α =(cosnϕ,sinnϕ) B= 2:
16 Stereographic projection: Rational map Skyrmions (N. S. Manton,C.Houghton and P. Sutcliffe) z=tan(θ/2)e iϕ ˆn z = 1 1+ z 2 (z+z, i(z z), 1 z 2 ) ˆn R : S 2 S 2 U =exp{if(r)ˆn R σ} ˆn R = 1 1+ R 2 (R+R, i(r R), 1 R 2 ) The holomorphic map of degree B: R=a(z)/b(z) R(z)= z4 +2i 3z 2 +1 B= 4: B= 7: (Octahedral Skyrmions) z 4 2i 3z 2 +1 B= 7:R(z)= z7 7z 5 7z 2 1 z 7 +7z 5 7z 2 +1 (Icosahedral Skyrmions)
17 R. A. Battye,, N. S. Manton, C.Houghton and P. Sutcliffe (1996,2004) Shell vs. Crystal Shell wins for m c 0.16
18 Skyrmion-antiSkyrmion chains (P. Sutcliffe, S.Krusch, Y.Shnir, T.Tchrakian ) φα = sin f sin g nα ; φ3 = sin f cos g ; φ4 = cos f ; θ=π Q = 12 n cos(mθ ) θ=0 = 12 n [1 ( 1)m ] f ( 0) = π, f ( ) = 0 r g (0) = 0, g ( ) = mπ
19 4 φ ( r, θ ) cos f ( r, θ ) (Skyrmion - antiskyrmion chains) Φ( r, θ ) 2 (MAM chains)
20 L= d 3 x Skyrmion-antiSkyrmion chains: mass term { } F 2 π 16 Tr(R µr µ ) 1 32e Tr([R 2 µ,r ν ][R µ,r ν ])+ m2 π F2 π 8 Tr(1 U) n=1 chains exist for m c 0.10
21 Skyrmions and instantons Skyrme field can be generated from the holonomy of a Yang-Mills instanton (M. Atiyah & N.Manton (1989), P. Sutcliffe (2010) { } U(x)=Pexp A U(x) : R 3 4 (x, x 4 )dx 4 SU(2) Baryon charge is equal to the Pontryagin charge: B= 1 24π 2 d 3 xε ijk Tr(R i R j R k ) N = 1 16π 2 Tr d 4 xf µν F µν Remarkable approximation to the exact solution of the Skyrme model (about 1%) Sakai-Sugimoto Sugimoto conjecture about a correspondence between Yang-Mills Mills-Chern- Simons instantons on a curved four-manifold and an extended Skyrme model (Skyrme( field and an infinite tower of massive vector mesons)
22 Summary and Outlook There is certain similarity between the monopoles and the Skyrmions. Rational maps approach works both for BPS monopoles and for Skyrmions. Axially-symmetric sphaleron solutions representing chains of solitons in alternating order exist in both models. Non-trival holonomy and Skyrmion-anti- Skyrmion chains? Skyrmed monopoles and rational maps? Gauged Skyrmions?
Skyrme model U : S 3 S 3. d 3 x. The Skyrme field: The topological charge: Q = 1. Rescaling: Sigma-model term Skyrme term Potential term.
Skyrme model The Skyrme field: U(r, t) r I U : S 3 S 3 L = f2 π 4 Tr µ U µ U + 1 32e 2 Tr U µ U,U ν U 2 f π = 186 MeV, m π = 136 MeV + m2 πf 2 π 8 Tr (U I) Sigma-model term Skyrme term Potential term The
More informationBaby Skyrmions in AdS 3 and Extensions to (3 + 1) Dimensions
Baby Skyrmions in AdS 3 and Extensions to (3 + 1) Dimensions Durham University Work in collaboration with Matthew Elliot-Ripley June 26, 2015 Introduction to baby Skyrmions in flat space and AdS 3 Discuss
More informationCharge quantization for dyons
Charge quantization for dyons Electron monopole pair (e,g( e,g) There is an elementary electric charge eg =n n Z e 0 = 1 g, e=ne 0 Pair of dyons: (e 1,g 1 ), (e 2,g 2 ): e 1 g 2 e 2 g 1 =n, n Z There is
More informationTopological Solitons from Geometry
Topological Solitons from Geometry Maciej Dunajski Department of Applied Mathematics and Theoretical Physics University of Cambridge Atiyah, Manton, Schroers. Geometric models of matter. arxiv:1111.2934.
More informationSolitons in the SU(3) Faddeev-Niemi Model
Solitons in the SU(3) Faddeev-Niemi Model Yuki Amari Tokyo University of Science amari.yuki.ph@gmail.com Based on arxiv:1805,10008 with PRD 97, 065012 (2018) In collaboration with Nobuyuki Sawado (TUS)
More informationA Review of Solitons in Gauge Theories. David Tong
A Review of Solitons in Gauge Theories David Tong Introduction to Solitons Solitons are particle-like excitations in field theories Their existence often follows from general considerations of topology
More informationSingular Monopoles and Instantons on Curved Backgrounds
Singular Monopoles and Instantons on Curved Backgrounds Sergey Cherkis (Berkeley, Stanford, TCD) C k U(n) U(n) U(n) Odense 2 November 2010 Outline: Classical Solutions & their Charges Relations between
More informationUNIVERSITI TEKNOLOGI MARA EXACT SOLUTIONS OF THE SU(2) YANG-MILLS-HIGGS THEORY
UNIVERSITI TEKNOLOGI MARA arxiv:hep-th/0006182v2 17 Jul 2000 EXACT SOLUTIONS OF THE SU(2) YANG-MILLS-HIGGS THEORY Rosy Teh PENANG-MALAYSIA July 2000 1 EXACT SOLUTIONS OF THE SU(2) YANG-MILLS-HIGGS THEORY
More informationAbelian and non-abelian Hopfions in all odd dimensions
Abelian and non-abelian Hopfions in all odd dimensions Tigran Tchrakian Dublin Institute for Advanced Studies (DIAS) National University of Ireland Maynooth, Ireland 7 December, 2012 Table of contents
More informationAdS Holography and dyonic black holes
AdS Holography and dyonic black holes Ya Shnir Thanks to my collaborators: O.Kichakova, J.Kunz and E.Radu Dubna,, 15 April 2014 Outline The gauge/gravity duality The AdS/CFT correspondence: a brief summary
More informationInstantons and Sphalerons in a Magnetic Field
Stony Brook University 06/27/2012 GB, G.Dunne & D. Kharzeev, arxiv:1112.0532, PRD 85 045026 GB, D. Kharzeev, arxiv:1202.2161, PRD 85 086012 Outline Motivation & some lattice results General facts on Dirac
More informationElectrically and Magnetically Charged Solitons in Gauge Field Th
Electrically and Magnetically Charged Solitons in Gauge Field Theory Polytechnic Institute of New York University Talk at the conference Differential and Topological Problems in Modern Theoretical Physics,
More informationSolitons and point particles
Solitons and point particles Martin Speight University of Leeds July 28, 2009 What are topological solitons? Smooth, spatially localized solutions of nonlinear relativistic classical field theories Stable;
More informationBaryon Physics in Holographic QCD Models (and Beyond) in collaboration with A. Wulzer
Baryon Physics in Holographic QCD Models (and Beyond) Alex Pomarol (Univ. Autonoma Barcelona) in collaboration with A. Wulzer One of the main goals of AdS/CFT: Find the string dual theory of QCD One of
More informationSkyrmions in models with pions and rho mesons
Skyrmions in models with pions and rho mesons Carlos Naya and Paul Sutcliffe arxiv:1803.06098v3 [hep-th] 4 Jun 2018 Department of Mathematical Sciences, Durham University, Durham DH1 3LE, United Kingdom.
More informationSolitons, Vortices, Instantons
Solitons, Vortices, Instantons Seminarvortrag von David Mroß Universität Bonn 1. Juni 2006 Seminar Theoretische Elementarteilchenphysik SS 06 Structure of the talk Solitons in a nutshell Recap: solitons
More informationInstanton constituents in sigma models and Yang-Mills theory at finite temperature
Instanton constituents in sigma models and Yang-Mills theory at finite temperature Falk Bruckmann Univ. of Regensburg Extreme QCD, North Carolina State, July 8 PRL (8) 56 [77.775] EPJ Spec.Top.5 (7) 6-88
More informationSupersymmetric Gauge Theories in 3d
Supersymmetric Gauge Theories in 3d Nathan Seiberg IAS Intriligator and NS, arxiv:1305.1633 Aharony, Razamat, NS, and Willett, arxiv:1305.3924 3d SUSY Gauge Theories New lessons about dynamics of quantum
More informationNucleons from 5D Skyrmions
Nucleons from 5D Skyrmions Giuliano Panico Physikalisches Institut der Universität Bonn Planck 2009 26 May 2009 Based on G. P. and A. Wulzer 0811.2211 [hep-ph] and A. Pomarol and A. Wulzer 0807.0316 [hep-ph]
More informationSYMMETRIC SKYRMIONS. Institute of Mathematics, University of Kent at Canterbury, Canterbury, CT2 7NZ, U.K.
UKC/IMS/97-07 IMPERIAL/TP/96-97/18 SYMMETRIC SKYRMIONS Richard A. Battye and Paul M. Sutcliffe Theoretical Physics Group, Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2BZ, UK.
More informationTopological Solitons
Nicholas Manton DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK email: N.S.Manton@damtp.cam.ac.uk Topological Solitons Lecture notes for the XIII
More informationarxiv:nlin/ v1 [nlin.si] 4 Dec 2000
Integrable Yang-Mills-Higgs Equations in 3-Dimensional De Sitter Space-Time. arxiv:nlin/24v [nlin.si] 4 Dec 2 V. Kotecha and R. S. Ward Department of Mathematical Sciences, University of Durham, Durham
More informationTopological reduction of supersymmetric gauge theories and S-duality
Topological reduction of supersymmetric gauge theories and S-duality Anton Kapustin California Institute of Technology Topological reduction of supersymmetric gauge theories and S-duality p. 1/2 Outline
More informationThe Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach)
The Role Of Magnetic Monopoles In Quark Confinement (Field Decomposition Approach) IPM school and workshop on recent developments in Particle Physics (IPP11) 2011, Tehran, Iran Sedigheh Deldar, University
More informationTwo-monopole systems and the formation of non-abelian clouds
Two-monopole systems and the formation of non-abelian clouds Changhai Lu* Department of Physics, Columbia University, New York, New York 10027 Received 14 July 1998; published 12 November 1998 We study
More informationContinuity of the Deconfinement Transition in (Super) Yang Mills Theory
Continuity of the Deconfinement Transition in (Super) Yang Mills Theory Thomas Schaefer, North Carolina State University 0.0 0.0 0.0 0.0 0.0 0.0 with Mithat Ünsal and Erich Poppitz Confinement and the
More informationNTNU Trondheim, Institutt for fysikk
NTNU Trondheim, Institutt for fysikk Examination for FY3464 Quantum Field Theory I Contact: Michael Kachelrieß, tel. 99890701 Allowed tools: mathematical tables Some formulas can be found on p.2. 1. Concepts.
More informationarxiv: v1 [hep-th] 10 Oct 2017
A direct test of the integral Yang-Mills equations through SU) monopoles C. P. Constantinidis, L. A. Ferreira and G. Luchini arxiv:171.3359v1 hep-th] 1 Oct 17 Departamento de Física Universidade Federal
More informationarxiv: v2 [hep-th] 15 Dec 2017
Spinning gravitating Skyrmions in generalized Einstein-Skyrme model I. Perapechka 1 and Ya. Shnir 1 Department of Theoretical Physics and Astrophysics, BSU, Minsk, Belarus Department of Theoretical Physics
More informationKink Chains from Instantons on a Torus
DAMTP 94-77 arxiv:hep-th/9409181v1 9 Sep 1994 Kink Chains from Instantons on a Torus Paul M. Sutcliffe Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge CB3 9EW,
More informationClassically isospinning Skyrmion solutions. Abstract
Classically isospinning Skyrmion solutions Richard A. Battye, 1, Mareike Haberichter, 2, and Steffen Krusch 2, 1 Jodrell Bank Centre for Astrophysics, University of Manchester, Manchester M13 9PL, U.K.
More informationt Hooft loop path integral in N = 2 gauge theories
t Hooft loop path integral in N = 2 gauge theories Jaume Gomis (based on work with Takuya Okuda and Vasily Pestun) Perimeter Institute December 17, 2010 Jaume Gomis (Perimeter Institute) t Hooft loop path
More informationA Multimonopole Solution in String Theory
CTP/TAMU-33/92 A Multimonopole Solution in String Theory arxiv:hep-th/9205051v2 15 May 1992 Ramzi R. Khuri Center for Theoretical Physics Texas A&M University College Station, TX 77843 A multimonopole
More informationSalty popcorn in a homogeneous low-dimensional toy model of holographic QCD
DCPT-16/43 Salty popcorn in a homogeneous low-dimensional toy model of holographic QCD Matthew Elliot-Ripley Department of Mathematical Sciences, Durham University, South Rd, Durham, UK arxiv:1610.09169v1
More informationContinuity of the Deconfinement Transition in (Super) Yang Mills Theory
Continuity of the Deconfinement Transition in (Super) Yang Mills Theory Thomas Schaefer, North Carolina State University 1.0 1.0 1.0 0.5 0.5 0.5 0.0 0.0 0.0 0.5 0.5 0.5 1.0 1.0 1.0 0.5 0.0 0.5 1.0 0.5
More informationQCD and Instantons: 12 Years Later. Thomas Schaefer North Carolina State
QCD and Instantons: 12 Years Later Thomas Schaefer North Carolina State 1 ESQGP: A man ahead of his time 2 Instanton Liquid: Pre-History 1975 (Polyakov): The instanton solution r 2 2 E + B A a µ(x) = 2
More informationarxiv:hep-th/ v2 7 Sep 1999
UKC/IMS/99/07 Monopoles and Harmonic Maps arxiv:hep-th/9903183v2 7 Sep 1999 Theodora Ioannidou and Paul M. Sutcliffe Institute of Mathematics, University of Kent at Canterbury, Canterbury, CT2 7NZ, U.K.
More informationSkyrme models- BPS and/or SUSY, at last
Skyrme models- BPS and/or SUSY, at last J.Sánchez-Guillén University of Santiago de Compostela Dual year Russia-Spain Particle, Nuclear and Astrop. Physics Barcelona, Nov 8-11, 2011 Contents The Problem:
More informationLight Nuclei as Quantized Skyrmions: Energy Spectra and Form Factors
Light Nuclei as Quantized Skyrmions: Energy Spectra and Form Factors N. S. Manton and S. W. Wood DAMTP, University of Cambridge, Wilberforce Road, Cambridge CB 0WA, United Kingdom Abstract We review the
More informationMath. Res. Lett. 13 (2006), no. 1, c International Press 2006 ENERGY IDENTITY FOR ANTI-SELF-DUAL INSTANTONS ON C Σ.
Math. Res. Lett. 3 (2006), no., 6 66 c International Press 2006 ENERY IDENTITY FOR ANTI-SELF-DUAL INSTANTONS ON C Σ Katrin Wehrheim Abstract. We establish an energy identity for anti-self-dual connections
More informationLectures on. Holographic QCD. Shigeki Sugimoto (Kavli IPMU) 1/53. holography 2013 APCTP, Pohang 2013/6/19 and 20
Lectures on Holographic QCD Shigeki Sugimoto (Kavli IPMU) Lecture @ holography 2013 APCTP, Pohang 2013/6/19 and 20 1/53 1 Introduction Claim : Hadrons can be described by string theory without using quarks
More informationHolographic Monopole Catalysis of Baryon Decay
Holographic Monopole Catalysis of Baryon Decay KIAS String Workshop, Sept. 22-26, 2008 Deog Ki Hong (Pusan Nat l U. ) Based on arxiv:0804.1326, done with K. Lee, C. Park, and H.U. Yee I. Introduction Gauge/String
More informationHolographic Entanglement Entropy for Surface Operators and Defects
Holographic Entanglement Entropy for Surface Operators and Defects Michael Gutperle UCLA) UCSB, January 14th 016 Based on arxiv:1407.569, 1506.0005, 151.04953 with Simon Gentle and Chrysostomos Marasinou
More informationS-CONFINING DUALITIES
DIMENSIONAL REDUCTION of S-CONFINING DUALITIES Cornell University work in progress, in collaboration with C. Csaki, Y. Shirman, F. Tanedo and J. Terning. 1 46 3D Yang-Mills A. M. Polyakov, Quark Confinement
More informationQuark Mass from Tachyon
Quark Mass from Tachyon Shigenori Seki This talk is based on O. Bergman, S.S., J. Sonnenschein, JHEP 071 (007) 07; S.S., JHEP 1007 (010) 091. 1 September 010 Crete Conference on Gauge Theories and the
More informationarxiv:hep-th/ v2 24 May 2001
Understanding Skyrmions using Rational Maps Nicholas S. Manton and Bernard M.A.G. Piette arxiv:hep-th/0008110v 4 May 001 Abstract. We discuss an ansatz for Skyrme fields in three dimensions which uses
More informationGeneral Relativity and Cosmology Mock exam
Physikalisches Institut Mock Exam Universität Bonn 29. June 2011 Theoretische Physik SS 2011 General Relativity and Cosmology Mock exam Priv. Doz. Dr. S. Förste Exercise 1: Overview Give short answers
More informationHopf Fibrations. Consider a classical magnetization field in R 3 which is longitidinally stiff and transversally soft.
Helmut Eschrig Leibniz-Institut für Festkörper- und Werkstofforschung Dresden Leibniz-Institute for Solid State and Materials Research Dresden Hopf Fibrations Consider a classical magnetization field in
More informationarxiv: v2 [hep-th] 21 Aug 2009
Preprint typeset in JHEP style - HYPER VERSION arxiv:0906.4961v2 [hep-th] 21 Aug 2009 Monopoles and flux strings from SU(2) adjoint scalars Chandrasekhar Chatterjee, Amitabha Lahiri chandra@bose.res.in,
More informationGeometry and Physics. Amer Iqbal. March 4, 2010
March 4, 2010 Many uses of Mathematics in Physics The language of the physical world is mathematics. Quantitative understanding of the world around us requires the precise language of mathematics. Symmetries
More informationMatryoshka Skyrmions, Confined Instantons and (P,Q) Torus Knots. Muneto Nitta (Keio Univ.)
Matryoshka Skyrmions, Confined Instantons and (P,Q) Torus Knots 20 th August 2013 Field theory and String theory @ YITP Muneto Nitta (Keio Univ.) 1[1] Phys.Rev.D86 (2012) 125004 [arxiv:1207.6958] [2] Phys.Rev.D87
More informationAcknowledgements An introduction to unitary symmetry The search for higher symmetries p. 1 The eight-baryon puzzle p. 1 The elimination of
Preface p. xiii Acknowledgements p. xiv An introduction to unitary symmetry The search for higher symmetries p. 1 The eight-baryon puzzle p. 1 The elimination of G[subscript 0] p. 4 SU(3) and its representations
More informationSolitons, Links and Knots
UKC/IMS/98-34 DAMTP-1998-110 Solitons, Links and Knots arxiv:hep-th/9811077v1 9 Nov 1998 Richard A. Battye and Paul M. Sutcliffe Department of Applied Mathematics and Theoretical Physics, University of
More informationSolitons and instantons in gauge theories
Solitons and instantons in gauge theories Petr Jizba FNSPE, Czech Technical University, Prague, Czech Republic ITP, Freie Universität Berlin, Germany March 15, 2007 From: M. Blasone, PJ and G. Vitiello,
More informationThe abundant richness of Einstein-Yang-Mills
The abundant richness of Einstein-Yang-Mills Elizabeth Winstanley Thanks to my collaborators: Jason Baxter, Marc Helbling, Eugen Radu and Olivier Sarbach Astro-Particle Theory and Cosmology Group, Department
More informationLARGE N c QCD AND THE SKYRME MODEL
LARGE N c QCD AND THE SKYRME MODEL Norberto Scoccola (CNEA Buenos Aires). Introduction: Hadrons. QCD as the theory of strong interactions. Asymptotic freedom and confinement. Non-perturbative QCD 1/N c
More informationPart III Classical and Quantum Solitons
Part III Classical and Quantum Solitons Based on lectures by N. S. Manton and D. Stuart Notes taken by Dexter Chua Easter 2017 Solitons are solutions of classical field equations with particle-like properties.
More informationMAP, MAC, and Vortex-rings Configurations in the Weinberg-Salam Model arxiv: v8 [hep-th] 20 Mar 2015
MAP, MAC, and Vortex-rings Configurations in the Weinberg-Salam Model arxiv:140.4v8 [hep-th] 0 Mar 015 Rosy Teh, Ban-Loong Ng and Khai-Ming Wong School of Physics, Universiti Sains Malaysia 11800 USM Penang,
More informationHolographic study of magnetically induced ρ meson condensation
Holographic study of magnetically induced ρ meson condensation Nele Callebaut Ghent University November 13, 2012 QCD in strong magnetic fields, Trento Overview 1 Introduction 2 Holographic set-up The Sakai-Sugimoto
More informationThe stability of the wall is due to the potential and the gradient balancing each other (Derrick s Theorem). Simple argument: = E grad
The stability of the wall is due to the potential and the gradient balancing each other (Derrick s Theorem). Simple argument: E grad ~ ( "# ) ~ $ & E pot ~ V (") ~ #$ 4 % ( ) * ~ $ Derrick s Theorem says
More informationAbelian vortices from Sinh Gordon and Tzitzeica equations
DAMTP-01-1 Abelian vortices from Sinh Gordon and Tzitzeica equations Maciej Dunajski Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3
More informationChiral Symmetry Breaking from Monopoles and Duality
Chiral Symmetry Breaking from Monopoles and Duality Thomas Schaefer, North Carolina State University with A. Cherman and M. Unsal, PRL 117 (2016) 081601 Motivation Confinement and chiral symmetry breaking
More informationSkyrmions up to Baryon Number 108
DAMTP-2012-62 Skyrmions up to Baryon Number 108 D.T.J. Feist, P.H.C. Lau and N.S. Manton arxiv:1210.1712v1 [hep-th] 5 Oct 2012 Department of Applied Mathematics and Theoretical Physics University of Cambridge
More informationarxiv:gr-qc/ v1 21 Mar 1996
Yang-Mills Inspired Solutions for General Relativity D. Singleton Department of Physics, Virginia Commonwealth University, Richmond, VA 23284-2000 arxiv:gr-qc/9603031v1 21 Mar 1996 (February 7, 2008) Abstract
More informationarxiv: v1 [hep-th] 27 Mar 2008
Noncanonicaly Embedded Rational Map Soliton in Quantum SU3 Skyrme Model D. Jurčiukonis and E.Norvaišas Vilnius University, Institute of Theoretical Physics and Astronomy, Goštauto, Vilnius 008, Lithuania
More informationInstanton Bags, High Density Holographic QCD and Chiral Symmetry Restoration
Instanton Bags, High Density Holographic QCD and Chiral Symmetry Restoration arxiv:1406.0205v2 [hep-th] 16 Oct 2014 S. Bolognesi Department of Physics E. Fermi and INFN, University of Pisa Largo Pontecorvo,
More informationMeson-Nucleon Coupling. Nobuhito Maru
Meson-Nucleon Coupling from AdS/QCD Nobuhito Maru (Chuo Univ.) with Motoi Tachibana (Saga Univ.) arxiv:94.3816 (Accepted in in EPJC) 7/9/9 workshop@yitp Plan 1: Introduction : Meson sector (review) 3:
More informationarxiv: v3 [hep-th] 11 Nov 2018
A mild source for the Wu-Yang magnetic monopole arxiv:1611.741v3 [hep-th] 11 Nov 218 C. P. Constantinidis, L. A. Ferreira and G. Luchini Departamento de Física Universidade Federal do Espírito Santo (UFES),
More informationarxiv: v4 [hep-th] 17 Aug 2017
Microscopic structure of the QCD vacuum D.G. Pak, 1, 2, Bum-Hoon Lee, 2, Youngman Kim, 5 Takuya Tsukioka, 6 and P.M. Zhang 1 1 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 70000, China
More informationPossible Advanced Topics Course
Preprint typeset in JHEP style - HYPER VERSION Possible Advanced Topics Course Gregory W. Moore Abstract: Potential List of Topics for an Advanced Topics version of Physics 695, Fall 2013 September 2,
More informationH-dibaryon in Holographic QCD. Kohei Matsumoto (M2, YITP) (in collaboration with Hideo Suganuma, Yuya Nakagawa)
H-dibaryon in Holographic QCD Kohei Matsumoto (M2, YITP) (in collaboration with Hideo Suganuma, Yuya Nakagawa) 1. Aug. 2016 1 Contents 1. Introduction 2. Chiral Soliton Model 3. Holographic QCD 4. Results
More information1/N Expansions in String and Gauge Field Theories. Adi Armoni Swansea University
1/N Expansions in String and Gauge Field Theories Adi Armoni Swansea University Oberwoelz, September 2010 1 Motivation It is extremely difficult to carry out reliable calculations in the strongly coupled
More informationThe E&M of Holographic QCD
The E&M of Holographic QCD Oren Bergman Technion and IAS O.B., G. Lifschytz, M. Lippert arxiv: 0802.3720, 080m.xxxx Also: Johnson, Kundu 0803.0038 Kim, Sin, Zahed 0803.0318 So you see, string theory provides
More informationLIBERATION ON THE WALLS IN GAUGE THEORIES AND ANTI-FERROMAGNETS
LIBERATION ON THE WALLS IN GAUGE THEORIES AND ANTI-FERROMAGNETS Tin Sulejmanpasic North Carolina State University Erich Poppitz, Mohamed Anber, TS Phys.Rev. D92 (2015) 2, 021701 and with Anders Sandvik,
More informationarxiv: v2 [hep-ph] 2 Dec 2016
Generalized Skyrme model with the loosely bound potential Sven Bjarke Gudnason, 1, Baiyang Zhang, 1, 2, 1, and Nana Ma 1 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China
More informationarxiv:hep-th/ v1 19 Feb 1995
Axially Symmetric Solutions for SU(2) Yang-Mills Theory D. Singleton Department of Physics, University of Virginia, Charlottesville, VA 22901 arxiv:hep-th/9502116v1 19 Feb 1995 (June 27, 2018) Abstract
More informationThe Higgs bundle moduli space
The Higgs bundle moduli space Nigel Hitchin Mathematical Institute University of Oxford Hamburg September 8th 2014 Add title here 00 Month 2013 1 re ut on 1977... INSTANTONS connection on R 4, A i (x)
More informationInstantons in string theory via F-theory
Instantons in string theory via F-theory Andrés Collinucci ASC, LMU, Munich Padova, May 12, 2010 arxiv:1002.1894 in collaboration with R. Blumenhagen and B. Jurke Outline 1. Intro: From string theory to
More informationVortices as Instantons in Noncommutative Discrete Space: Use of Z 2 Coordinates
Vortices as Instantons in Noncommutative Discrete Space: Use of Z Coordinates arxiv:0904.1848v [hep-th] 14 Jul 009 Hideharu Otsu Faculty of Economics, Aichi University, Toyohashi, Aichi 441-85, Japan Toshiro
More informationEinstein-Maxwell-Chern-Simons Black Holes
.. Einstein-Maxwell-Chern-Simons Black Holes Jutta Kunz Institute of Physics CvO University Oldenburg 3rd Karl Schwarzschild Meeting Gravity and the Gauge/Gravity Correspondence Frankfurt, July 2017 Jutta
More informationLattice Gauge Theory and the Maxwell-Klein-Gordon equations
Lattice Gauge Theory and the Maxwell-Klein-Gordon equations Tore G. Halvorsen Centre of Mathematics for Applications, UiO 19. February 2008 Abstract In this talk I will present a discretization of the
More informationPoS(Confinement X)058
Confining gauge theories with adjoint scalars on R 3 S 1 University of Bielefeld E-mail: nishimura@physik.uni-bielefeld.de Michael Ogilvie Washington University, St. Louis E-mail: mco@physics.wustl.edu
More informationTransparent connections
The abelian case A definition (M, g) is a closed Riemannian manifold, d = dim M. E M is a rank n complex vector bundle with a Hermitian metric (i.e. a U(n)-bundle). is a Hermitian (i.e. metric) connection
More informationMonopoles and Confinement
Monopoles and Confinement Raquel Queiroz under the supervision of Dr. Arttu Rajantie Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London London,
More informationTopological zero modes at finite chemical potential
Topological zero modes at finite chemical potential Falk Bruckmann (Univ. Regensburg) Sign 2012, Regensburg, Sept. 2012 with Rudi Rödl, Tin Sulejmanpasic (paper in prep.) Falk Bruckmann Topological zero
More informationChern-Simons Theory and Its Applications. The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee
Chern-Simons Theory and Its Applications The 10 th Summer Institute for Theoretical Physics Ki-Myeong Lee Maxwell Theory Maxwell Theory: Gauge Transformation and Invariance Gauss Law Charge Degrees of
More informationHIGH DENSITY NUCLEAR CONDENSATES. Paulo Bedaque, U. of Maryland (Aleksey Cherman & Michael Buchoff, Evan Berkowitz & Srimoyee Sen)
HIGH DENSITY NUCLEAR CONDENSATES Paulo Bedaque, U. of Maryland (Aleksey Cherman & Michael Buchoff, Evan Berkowitz & Srimoyee Sen) What am I talking about? (Gabadadze 10, Ashcroft 89) deuterium/helium at
More informationMagnetic monopoles. Arjen Baarsma. January 14, 2009
Magnetic s Arjen Baarsma January 14, 2009 GUT s GUT s 2 GUT s GUT s 3 (very briefly) Thoroughly discussed in previous talks Spontaneous symmetry occurs when a system with some symmetry (described by a
More informationChern-Simons gauge theory The Chern-Simons (CS) gauge theory in three dimensions is defined by the action,
Lecture A3 Chern-Simons gauge theory The Chern-Simons (CS) gauge theory in three dimensions is defined by the action, S CS = k tr (AdA+ 3 ) 4π A3, = k ( ǫ µνρ tr A µ ( ν A ρ ρ A ν )+ ) 8π 3 A µ[a ν,a ρ
More informationIntegrable spin systems and four-dimensional gauge theory
Integrable spin systems and four-dimensional gauge theory Based on 1303.2632 and joint work with Robbert Dijkgraaf, Edward Witten and Masahito Yamizaki Perimeter Institute of theoretical physics Waterloo,
More informationThink Globally, Act Locally
Think Globally, Act Locally Nathan Seiberg Institute for Advanced Study Quantum Fields beyond Perturbation Theory, KITP 2014 Ofer Aharony, NS, Yuji Tachikawa, arxiv:1305.0318 Anton Kapustin, Ryan Thorngren,
More informationExact Solutions of 2d Supersymmetric gauge theories
Exact Solutions of 2d Supersymmetric gauge theories Abhijit Gadde, IAS w. Sergei Gukov and Pavel Putrov UV to IR Physics at long distances can be strikingly different from the physics at short distances
More informationHairy black holes in general Skyrme models
Hairy black holes in general Skyrme models C. Adam University of Santiago de Compostela SIG5, Krakow, June 2016 based on C. Adam, O. Kichakova, Ya. Shnir, A. Wereszczynski, "Hairy black holes in the general
More informationShow, for infinitesimal variations of nonabelian Yang Mills gauge fields:
Problem. Palatini Identity Show, for infinitesimal variations of nonabelian Yang Mills gauge fields: δf i µν = D µ δa i ν D ν δa i µ..) Begin by considering the following form of the field strength tensor
More informationINSTANTON MODULI AND COMPACTIFICATION MATTHEW MAHOWALD
INSTANTON MODULI AND COMPACTIFICATION MATTHEW MAHOWALD () Instanton (definition) (2) ADHM construction (3) Compactification. Instantons.. Notation. Throughout this talk, we will use the following notation:
More informationGeometry and Spin Transport in Skyrmion Magnets
Geometry and Spin Transport in Skyrmion Magnets Benjamin Brown University of Warwick Conference of Astronomy and Physics Students, University College London, 2017 What is a Magnetic Skyrmion? What is a
More informationTwo Fundamental Principles of Nature s Interactions
Two Fundamental Principles of Nature s Interactions Tian Ma, Shouhong Wang Supported in part by NSF, ONR and Chinese NSF http://www.indiana.edu/ fluid I. Gravity and Principle of Interaction Dynamics PID)
More informationA BPS Skyrme model. Journal of Physics: Conference Series. Related content. To cite this article: C Adam et al 2011 J. Phys.: Conf. Ser.
Journal of Physics: Conference Series A BPS Skyrme model To cite this article: C Adam et al 2011 J. Phys.: Conf. Ser. 284 012006 View the article online for updates and enhancements. Related content -
More informationAxions. Kerstin Helfrich. Seminar on Theoretical Particle Physics, / 31
1 / 31 Axions Kerstin Helfrich Seminar on Theoretical Particle Physics, 06.07.06 2 / 31 Structure 1 Introduction 2 Repetition: Instantons Formulae The θ-vacuum 3 The U(1) and the strong CP problem The
More informationOn Consistency in the Skyrme Topological Model
On Consistency in the Skyrme Topological Model Syed Afsar Abbas Centre for Theoretical Physics, JMI University, New Delhi - 11005, India and Jafar Sadiq Research Institute AzimGreenHome, NewSirSyed Nagar,
More information