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Proof of Quark Confinement and Baryon-Antibaryon Duality

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Proof of Quark Confinement and Baryon-Antibaryon Duality Proof of quark confinement and baryon-antibaryon duality: I: Gauge symmetry breaking in dual 4D fractional quantum Hall superfluidic space-time A. E. Inopin1 and N. O. Schmidt2 1Department of Experimental Nuclear Physics, Karazin National University, Svobody Sq. 4, Kharkiv, 61077, Ukraine (E-mail: [email protected]) 2Department of Mathematics, Boise State University, 1910 University Drive, Boise, Idaho, 83725, USA (E-mail: [email protected]) (Dated: October 2012) We prove quark (and antiquark) confinement for a baryon-antibaryon pair and design a well- defined, easy-to-visualize, and simplified mathematical framework for particle and astro physics based on experimental data. From scratch, we assemble a dual 4D space-time topology and gen- eralized coordinate system for the Schwarzschild metric. Space-time is equipped with “fractional quantum number order parameter fields” and topological defects for the simultaneous and sponta- neous breaking of several symmetries, which are used to construct the baryon wavefunction and its corresponding antisymmetric tensor. The confined baryon-antibaryon pair is directly connected to skyrmions with “massive ‘Higgs-like’ scalar amplitude-excitations” and “massless Nambu-Goldstone pseudo-scalar phase-excitations”. Newton’s second law and Einstein’s relativity are combined to de- fine a Lagrangian with effective potential and effective kinetic. We prove that our theory upgrades the prediction precision and accuracy of QCD/QED and general relativity, implements 4D versions of string theory and Witten’s M-theory, and exemplifies M.C. Escher’s duality. I. INTRODUCTION ring “cancel out” due to the CPT-Theorem. Spontaneous symmetry breaking (SSB) generates massless “Nambu- Quarks and antiquarks are the fundamental building Goldstone pseudo-scalar phase-excitations” [10–13] and blocks of baryons and antibaryons, respectively. To date, massive “Higgs-like scalar amplitude-excitations” [14] of nature presents an impressive display of mass-energy puz- Laughlin statistics [3]. First, we provide conceptual zles in physics, including the creation, annihilation, and quark confinement proof in Section II. Second, we pro- confinement of baryons and antibaryons. The mystery vide mathematical quark confinement proof in Sections of quark confinement is a colossal problem in physics; III, IV, V, and VI. it is the phenomenon that color charged particles (such In Section II, we prepare for our quark confine- as quarks) cannot be isolated singularly, and therefore ment proof by conceptually aligning the reader to cannot be directly observed [1]. In this first paper of the our 4D FQHS space-time scenario. We investigate series, we hunt down this “Great Beast” and prove quark- the two dynamical scales that arise in the double- antiquark confinement for a baryon-antibaryon pair in a confinement, double-stereographic gravitational super- 4D space-time, where the dimension of time is circular lensing, and double-horizons inherent to baryons and an- rather than linear. We attack the problem from multiple tibaryons. We prove that a baryon-antibaryon pair is perspectives simultaneously to establish a well-defined composed of three distinct quark-antiquark pairs, which gauge theory equipped with Legget’s superfluid configu- form three corresponding “thin color-electric flux tubes” ration of Landau’s order parameter fields [2], Laughlin’s [15] of Laughlin excitations [3] and fractional statistics quasiparticles [3], a baryon wavefunction, antisymmetric [16]. We discuss the hadronization process and the mod- tensors, and more. From scratch, we construct a topo- ified Gribov QED/QCD vacuum, where all properties in logical solution and Lagrangian that intertwines Newto- 3D Schwarzschild space can be inferred from the analogue nian [4] and Einsteinian concepts [5], improves the pre- of the 2D gauge field on the six-coloring kagome lattice dictive capability of quantum chromo-dynamics (QCD) manifold. Additionally, we venture to the interaction be- and quantum electro-dynamics (QED) [6], reduces di- tween the boson propagators and gravity by introducing mensional complexity of string theory and M-theory [7], “gravitational birefringence”. exhibits M.C. Escher’s duality [8], and is directly sup- In Section III, we begin mathematically constructing ported by a diverse experimental array. In short, the dual the topology and framework for our quark confinement baryon and antibaryon quantum states are encoded with proof in FQHS. We discuss the surface and generalized quantum number order parameters of fractional statistics Riemann coordinates used to encode our FQHS space- for quasiparticles with baryon wavefunction antisymme- time. We extend the definition of complex numbers and try. We prove quark-antiquark confinement in terms of use them to represent locations on the 1D Riemann sur- Laughlin excitations [3] that dynamically arise due to face; we prove that the complex numbers are both scalars our fractional quantum Hall superfluidic (FQHS) space- and Euclidean vectors. We define axis constraints for time and topology inspired by the quasiparticle inter- the vectors, which let us construct a powerful 2D gen- ferometer experiments of Goldman [9]. We prove that eralized coordinate system on the surface equipped with the quarks and antiquarks confined to the holographic the Pythagorean identity; the locations may always be The Hadronic Journal • Volume 35 • Number 5 • October 2012 expressed in terms of right triangles with real and imag- II. ALIGNMENT TO CONFINEMENT: inary components. CONCEPTUAL PROOF In Section IV, we explore the three distinct topologi- cal sub-surface zones for a baryon and antibaryon using At the Fermi scale, a baryon’s event horizon confine- set and group theory. We formally define the zones us- ment radius baryon = 2Mbaryon strongly depends on it’s ing trichotomy and our generalized coordinates for 2D mass Mbaryon, which can vary in size in accordance to and 3D space. We prove that the time-like region is a its quark composition identified by the Standard Model. holographic ring—a closed curve and simple contour of This is known as baryon confinement (for three-quark points, which can be scaled to, for example, the Fermi confinement) and is modeled as a baryon bag. Simi- radius. We formally define space and time as being dual. larly, an antibaryon’s event horizon confinement radius Additionally, we demonstrate that the time-like region antibaryon = 2Mantibaryon strongly depends on it’s mass represents the U(1) and SU(2) symmetry groups, which Mantibaryon. This is known as antibaryon confinement is isomorphic to the SO(3) orthogonal group; all 3D prop- (for three-antiquark confinement) and is modeled as an erties are inferred directly from the 2D holographic ring antibaryon bag. A baryon and its antibaryon merge to re- for the SU(2) gauged Bose-Einstein condensate. flect three-pair quark-antiquark confinement. For exam- In Section V, we define the Baryon Wavefunction ple in a proton-antiproton pair, an antiproton of antimass (BWF) of fractional quantum number order parameters Mantibaryon = Mantiproton = 1 GeV precisely counterbal- (OP) for our quark (q) and antiquark (q¯) confinement ances a proton of mass Mbaryon = Mproton = 1 GeV due proof. Additionally, we discuss the amplitude-excitations to antiferromagnetic ordering and the CPT-Theorem. [14] and phase-excitations [10–13] for Laughlin quasipar- On this scale we identify the general mechanism, namely ticles [3] experienced by the BWF OPs in our FQHS Baryon-Antibaryon Confinement (BAC), which is re- space-time scenario. For this, we express the full BWF sponsible for the dynamics. It is based on the appear- antisymmetries and CPT-transformations. ance of a critical radius 2M = baryon = antibaryon for In Section VI, we express the Lagrangian in terms of ef- quark-antiquark confinement at the 1 Fermi scale and fective potential and effective kinetic for our FQHS space- the appropriate generalized dynamics—effective gravito- time scenario. For this, we apply both Newtonian and strong interaction. So in gravity plus electromagnetism, Einsteinian concepts to the q and q¯ confinement proof there is one interesting mechanism—radiation trapping and thereby incorporate effective force, effective mass, just on the horizon’s surface, that is a coherent particle and effective acceleration. accumulation structure [18] of fractional statistics and toroidal vortex [20]. The toroidal vortex, that stores in- In Section VII, we prepare a concise correspondence formation as in the holographic hypothesis [15], inter- to the authors of the Yuan-Mo-Wang (YMW) baryon- twines the baryon and antibaryon confinement mecha- antibaryon SU(3) model [17]. In doing so, we relay the nisms, creating BAC. The toroidal vortex forms between importance of the YMW model and report on a number the spherical shells defined at the inner confinement ra- of similarities between it and our confinement scenario. dius and the outer confinement radius = 3M Additionally, we contrast the models by identifying key 2M 3M (based on the effective potential); 2M and 3M corre- distinctions and suggest that our model may upgrade the spond to the “horizon” and “imaginary surface”, respec- YMW model’s state space and accuracy, and thereby ex- tively, in Figure 6 of Witten [15]; there are two distinct tend its prediction horizon. Ultimately, we realize that quantum critical points imposed by an antibaryon or both constructions exhibit remarkable similarities, and baryon for the double-stereographic gravitational super- that it may be possible in the
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