Light-Front Holography in QCD and Hadronic Physics
Light-Front Holography in QCD and Hadronic Physics
Guy F. de Teramond´
Universidad de Costa Rica
Rencontres de Moriond
QCD and High Energy Interactions
La Thuile, Valle d’Aosta, Italy
March 22-29, 2014
Image credit: N. Evans
In collaboration with Stan Brodsky (SLAC) and Hans G. Dosch (Heidelberg)
Page 1 Moriond 2014, QCD and High Energy Interactions, La Thuile, March 25, 2013 Light-Front Holography in QCD and Hadronic Physics
Introduction
• SLAC and DESY 70’s: elementary interactions of quarks and gluons at short distances remarkably well described by QCD
• No understanding of large distance strong dynamics of QCD: how quarks and gluons are confined and how hadrons emerge as asymptotic states
• Euclidean lattice important first-principles numerical simulation of nonperturbative QCD: excitation spectrum of hadrons requires enormous computational complexity beyond ground-state configurations
• Only known analytically tractable treatment in relativistic QFTh is perturbation theory
• Important theoretical goal: find initial analytic approximation to strongly coupled QCD, like Schrodinger¨ or Dirac Eqs in atomic physics, corrected for quantum fluctuations
• Convenient frame-independent Hamiltonian framework for treating bound-states in relativistic theories (including well defined massless quark limit) is light-front (LF) quantization
• To a first semiclassical approximation one can reduce the strongly correlated multi-parton LF dynamics to an effective one-dim QFTh, which encodes the conformal symmetry of the classical QCD Lagrangian
Page 2 Moriond 2014, QCD and High Energy Interactions, La Thuile, March 25, 2013 Light-Front Holography in QCD and Hadronic Physics
• Effective LF theory for QCD endowed with SO(2, 1) algebraic structure follows from one-dim semiclassical 4 – dim Light – 5 – dim Front Dynamics Classical Gravity approximation to LF dynamics in physical space-time, higher dimensional gravity in AdS space and 5 LFD AdS5 one-dimensional conformal quantum mechanics
• Result is a relativistic LF wave equation with a confining LFQM AdS2 SO(2,1) structure which incorporates essential spectroscopic and dynamical features of hadron physics Conf(R1) • Remarkable connection follows from isomorphism of 1 one-dim conformal group Conf R with SO(2, 1), dAFF
which is also the isometry group of AdS2 1 – dim 1-2014 • One of the generators of SO(2, 1) is compact and 8840A1 Quantum Field Theory has therefore a discrete spectrum !
Conformal Quantum Mechanics: de Alfaro, Fubini and Furlan (dAFF)
Page 3 Moriond 2014, QCD and High Energy Interactions, La Thuile, March 25, 2013 Light-Front Holography in QCD and Hadronic Physics
Dirac Forms of Relativistic Dynamics [Dirac (1949)]
• Poincare´ generators P µ and M µν separated into kinematical and dynamical
• Kinematical generators act along initial hypersurface and contain no interactions
• Dynamical generators are responsible for evolution of the system and depend on the interactions
• Each front has its Hamiltonian and evolve (a)ct (b)ct (c) ct with a different time, but results computed z z z in any front should be identical y y y (different parameterizations of space-time) 8-2013 8811A4
• Instant form: initial surface defined by x0 = 0: P 0, K dynamical, P, J kinematical
• Front form: initial surface tangent to the light cone x+ = x0 + x3 = 0 ( P ± = P 0 ± P 3)
− x y 3 P ,J ,J dynamical P⊥,J , K kinematical
• Point form: initial surface is the hyperboloid x2 = κ2 > 0, x0 > 0: P µ dynamical,M µν kinematical
Page 4 Moriond 2014, QCD and High Energy Interactions, La Thuile, March 25, 2013 Light-Front Holography in QCD and Hadronic Physics
Light-Front Dynamics
+ − ± 0 3 • Hadron with 4-momentum P = (P ,P , P⊥), P = P ± P , mass-shell relation µ 2 PµP = M leads to LF Hamiltonian equation M 2 + P2 P −|ψ(P )i = ⊥ |ψ(P )i P +
µ − + 2 + • Construct LF invariant Hamiltonian PµP = P P − P⊥ (P and P⊥ kinematical)
µ 2 PµP |ψ(P )i = M |ψ(P )i
+ + • Longitudinal momentum P is kinematical: sum of single particle constituents pi of bound state, + P + + P = i pi , pi > 0 − Pn − • Bound-state is arbitrarly off the LF energy shell, P − i pi < 0
• Vacuum is the state with P + = 0 and contains no particles: all other states have P + > 0
• Simple structure of vacuum allows definition of partonic content of hadron in terms of wavefunctions: quantum-mechanical probabilistic interpretation of hadronic states
Page 5 Moriond 2014, QCD and High Energy Interactions, La Thuile, March 25, 2013 Light-Front Holography in QCD and Hadronic Physics
Semiclassical Approximation to QCD in the Light Front [GdT and S. J. Brodsky, PRL 102, 081601 (2009)]
• Reduce effectively LF multiparticle dynamics to a 1-dim QFT with no particle creation and absorption: LF quantum mechanics !
• Central problem is derivation of effective interaction which acts only on the valence sector: express higher Fock states as functionals of the lower ones
2 0 µ 2 0 • Compute M from hadronic matrix element hψ(P )|PµP |ψ(P )i=M hψ(P )|ψ(P )i
• Semiclassical approximation