11 research outputs found
Kinematical and Dynamical Aspects of Higher-Spin Bound-State Equations in Holographic QCD
In this paper we derive holographic wave equations for hadrons with arbitrary
spin starting from an effective action in a higher-dimensional space asymptotic
to anti-de Sitter (AdS) space. Our procedure takes advantage of the local
tangent frame, and it applies to all spins, including half-integer spins. An
essential element is the mapping of the higher-dimensional equations of motion
to the light-front Hamiltonian, thus allowing a clear distinction between the
kinematical and dynamical aspects of the holographic approach to hadron
physics. Accordingly, the non-trivial geometry of pure AdS space encodes the
kinematics, and the additional deformations of AdS space encode the dynamics,
including confinement. It thus becomes possible to identify the features of
holographic QCD which are independent of the specific mechanisms of conformal
symmetry breaking. In particular, we account for some aspects of the striking
similarities and differences observed in the systematics of the meson and
baryon spectra.Comment: 43 page
Threefold Complementary Approach to Holographic QCD
A complementary approach, derived from (a) higher dimensional anti--de Sitter
(AdS) space, (b) light-front quantization and (c) the invariance properties of
the full conformal group in one dimension leads to a nonperturbative
relativistic light-front wave equation which incorporates essential
spectroscopic and dynamical features of hadron physics. The fundamental
conformal symmetry of the classical QCD Lagrangian in the limit of massless
quarks is encoded in the resulting effective theory. The mass scale for
confinement emerges from the isomorphism between the conformal group and
SO(2,1). This scale appears in the light-front Hamiltonian by mapping to the
evolution operator in the formalism of de Alfaro, Fubini and Furlan, which
retains the conformal invariance of the action. Remarkably, the specific form
of the confinement interaction and the corresponding modification of AdS space
are uniquely determined in this procedure.Comment: Reference added. Article accepted for publication in PL
QCD on the Light-Front -- A Systematic Approach to Hadron Physics
Light-Front Hamiltonian theory provides a rigorous frame-independent
framework for solving nonperturbative QCD. The valence Fock-state wavefunctions
of the light-front QCD Hamiltonian satisfy a single-variable relativistic
equation of motion, analogous to the nonrelativistic radial Schr\"odinger
equation, with an effective confining potential U which systematically
incorporates the effects of higher quark and gluon Fock states. Remarkably, the
potential U has a unique form of a harmonic oscillator potential if one
requires that the chiral QCD action remains conformally invariant. A mass gap
arises when one extends the formalism of de Alfaro, Fubini and Furlan to
light-front Hamiltonian theory. The valence LF meson wavefunctions for zero
quark mass satisfy a single-variable relativistic equation of motion in the
invariant variable , which is conjugate to the
invariant mass squared. The result is a nonperturbative relativistic
light-front quantum mechanical wave equation which incorporates color
confinement and other essential spectroscopic and dynamical features of hadron
physics, including a massless pion for zero quark mass and linear Regge
trajectories with the same slope in the radial quantum number n and orbital
angular momentum L. The corresponding light-front Dirac equation provides a
model of nucleons. The same light-front equations arise from the holographic
mapping of the soft-wall model modification of AdS_5 space with a unique
dilaton profile to QCD (3+1) at fixed light-front time. Light-front holography
thus provides a precise relation between amplitudes in the fifth dimension of
AdS space and light-front wavefunctions. We also discuss the implications of
the underlying conformal template of QCD for renormalization scale-setting, and
the implications of light-front quantization for the value of the cosmological
constant.Comment: Invited talk, presented by SJB at LightCone 2013+, May 20- May 24,
2013, Skiathos, Greece. arXiv admin note: text overlap with arXiv:1309.4856,
arXiv:1308.5251, arXiv:1302.539
Light-Front Holographic QCD and the Confinement Potential
Light-Front Hamiltonian theory, derived from the quantization of the QCD
Lagrangian at fixed light-front time \tau = t+z/c, provides a rigorous
frame-independent framework for solving nonperturbative QCD. The eigenvalues of
the light-front QCD Hamiltonian predict the hadronic mass spectrum, and the
eigensolutions provide the light-front wavefunctions describing hadron
structure. The valence Fock-state wavefunctions of the light-front QCD
Hamiltonian satisfy a single-variable relativistic equation of motion,
analogous to the nonrelativistic radial Schrodinger equation, with an effective
confining potential U which systematically incorporates the effects of higher
quark and gluon Fock states. The potential U has a unique form if one requires
that the action for zero quark mass remains conformally invariant. The
holographic mapping of gravity in AdS space to QCD with a specific soft-wall
dilaton yields the same light-front Schrodinger equation. It also gives a
precise relation between the bound-state amplitudes in the fifth dimension z of
AdS space and the boost-invariant light-front wavefunctions describing the
internal structure of hadrons in physical space-time. The elastic and
transition form factors of the pion and the nucleons are found to be well
described in this framework. The predictions include a zero-mass pion in the
chiral limit, and linear Regge trajectories with the same slope in the radial
quantum number n and orbital angular momentum L. The light-front AdS/QCD
holographic approach thus gives a frame-independent representation of
color-confining dynamics and the excitation spectra of light-quark hadrons in
terms of a single mass parameter. We also discuss the implications of the
underlying conformal template of QCD for renormalization scale-setting and the
implications of light-front quantization for the value of the cosmological
constant.Comment: Presented by SJB at Light-Cone 2012: Relativistic Hadronic and
Particle Physics, 10 to 15 December, 2012 at the University of Delhi, New
Delhi, Indi
Conformal Symmetry, Confinement, and Light-Front Holographic QCD
We show that (a) the conformal properties of Anti-de Sitter (AdS) space, (b)
the properties of a field theory in one dimension under the full conformal
group found by de Alfaro, Fubini and Furlan, and (c) the frame-independent
single-variable light-front Schr\"odinger equation for bound states all lead to
the same result: a relativistic nonperturbative model which successfully
incorporates salient features of hadronic physics, including confinement,
linear Regge trajectories, and results which are conventionally attributed to
spontaneous chiral symmetry breaking.Comment: Presented by SJB at the Third Workshop on the QCD Structure of the
Nucleon (QCD-N'12), Bilbao, Spain, October 22-26, 2012. This work was
supported by the Department of Energy contract DE--AC02--76SF0051
Modified Anti-de-Sitter Metric, Light-Front Quantized QCD, and Conformal Quantum Mechanics
We briefly review the remarkable connections between light-front QCD, gravity
in AdS space, and conformal quantum mechanics. We discuss, in particular, the
group theoretical and geometrical aspects of the underlying one-dimensional
quantum field theory. The resulting effective theory leads to a
phenomenologically successful confining interaction potential in the
relativistic light-front wave equation which incorporates relevant
non-perturbative dynamical aspects of hadron physics.Comment: 12 pages, 2 figures. Presented by HGD at the International Fall
Workshop Geometry and Physics II, Institut Henri Poincare, Paris, November 28
and 29, 201