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Light-Front Holographic QCD and Emerging Confinement

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Light-Front Holographic QCD and Emerging Confinement Physics Reports ( ) – Contents lists available at ScienceDirect Physics Reports journal homepage: www.elsevier.com/locate/physrep Light-front holographic QCD and emerging confinement Stanley J. Brodsky a,∗, Guy F. de Téramond b, Hans Günter Dosch c, Joshua Erlich d a SLAC National Accelerator Laboratory, Stanford University, Stanford, CA 94309, USA b Universidad de Costa Rica, San José, Costa Rica c Institut für Theoretische Physik, Philosophenweg 16, D-69120 Heidelberg, Germany d College of William and Mary, Williamsburg, VA 23187, USA article info a b s t r a c t Article history: In this report we explore the remarkable connections between light-front dynamics, its Accepted 1 May 2015 holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and Available online xxxx conformal quantum mechanics. This approach provides new insights into the origin of a editor: J.A. Bagger fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical space–time. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q2 the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q2 the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications. ' 2015 Elsevier B.V. All rights reserved. Contents 1. Introduction.............................................................................................................................................................................................3 1.1. Motivation...................................................................................................................................................................................3 1.2. The AdS/CFT correspondence and holographic QCD ................................................................................................................4 1.3. Light-front holographic QCD......................................................................................................................................................6 1.4. Confinement and conformal algebraic structures ....................................................................................................................7 ∗ Corresponding author. E-mail addresses: [email protected] (S.J. Brodsky), [email protected] (G.F. de Téramond), [email protected] (H.G. Dosch), [email protected] (J. Erlich). http://dx.doi.org/10.1016/j.physrep.2015.05.001 0370-1573/' 2015 Elsevier B.V. All rights reserved. 2 S.J. Brodsky et al. / Physics Reports ( ) – 1.5. Other approaches and applications ...........................................................................................................................................8 1.6. Contents of this review...............................................................................................................................................................9 2. A semiclassical approximation to light-front quantized QCD..............................................................................................................9 2.1. The Dirac forms of relativistic dynamics................................................................................................................................... 11 2.2. Light-front dynamics.................................................................................................................................................................. 12 2.3. Light-front quantization of QCD ................................................................................................................................................ 12 2.3.1. Representation of hadrons in the light-front Fock basis........................................................................................... 14 2.4. Semiclassical approximation to QCD in the light front ............................................................................................................ 15 2.4.1. Inclusion of light quark masses .................................................................................................................................. 18 3. Conformal quantum mechanics and light-front dynamics .................................................................................................................. 19 3.1. One-dimensional conformal field theory.................................................................................................................................. 19 3.2. Connection to light-front dynamics .......................................................................................................................................... 22 3.3. Conformal quantum mechanics, SO.2; 1/ and AdS2 ................................................................................................................. 23 4. Higher-spin wave equations and AdS kinematics and dynamics ........................................................................................................ 24 4.1. Scalar and vector fields............................................................................................................................................................... 24 4.2. Arbitrary integer spin ................................................................................................................................................................. 26 4.2.1. Confining interaction and warped metrics ................................................................................................................ 28 4.2.2. Higher spin in a gauge invariant AdS model.............................................................................................................. 28 4.3. Arbitrary half-integer spin ......................................................................................................................................................... 29 5. Light-front holographic mapping and hadronic spectrum................................................................................................................... 30 5.1. Integer spin ................................................................................................................................................................................. 31 5.1.1. A light-front holographic model for mesons ............................................................................................................. 32 5.1.2. Meson spectroscopy in a gauge invariant AdS model............................................................................................... 35 5.1.3. Light quark masses and meson spectrum.................................................................................................................. 35 5.2. Half-integer spin......................................................................................................................................................................... 38 5.2.1. A light-front holographic model for baryons............................................................................................................. 39 6. Light-front holographic mapping and transition amplitudes .............................................................................................................. 42 6.1. Meson electromagnetic form factor .......................................................................................................................................... 43 6.1.1. Meson form factor in AdS space ................................................................................................................................. 43 6.1.2. Meson form factor in light-front QCD ........................................................................................................................ 44 6.1.3. Light-front holographic mapping ............................................................................................................................... 44 6.1.4. Soft-wall form factor model........................................................................................................................................ 47 6.1.5. Time-like form factors in holographic QCD ..............................................................................................................
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