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Register a new userThe AdS/CFT Correspondence and Light-Front QCD
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We identify an invariant light-front coordinate $zeta$ which allows the separation of the dynamics of quark and gluon binding from the kinematics of constituent spin and internal orbital angular momentum. The result is a single-variable light-front Schrodinger equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This frame-independent light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-$J$ modes on anti-de Sitter (AdS) space. Light-front holography is a remarkable feature of AdS/CFT: it allows hadronic amplitudes in the AdS fifth dimension to be mapped to frame-independent light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons at the amplitude level. In principle, the model can be systematically improved by diagonalizing the full QCD light-front Hamiltonian on the AdS/QCD basis. Quark and gluon hadronization can be computed at the amplitude level by convoluting the off-shell $T$ matrix calculated from the QCD light-front Hamiltonian with the hadronic light-front wavefunctions. We also note the distinction between static observables such as the probability distributions computed from the square of the light-front wavefunctions versus dynamical observables such as the structure functions and the leading-twist single-spin asymmetries measured in deep inelastic scattering which include the effects of initial and final-state interactions.
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Starting from the Hamiltonian equation of motion in QCD we find a single variable light-front equation for QCD which determines the eigenspectrum and the light-front wavefunctions of hadrons for general spin and orbital angular momentum. This light-front wave equation is equivalent to the equations of motion which describe the propagation of spin-$J$ modes on anti-de Sitter (AdS) space.
We study, using the dual AdS description, the vacua of field theories where some of the gauge symmetry is broken by expectation values of scalar fields. In such vacua, operators built out of the scalar fields acquire expectation values, and we show how to calculate them from the behavior of perturbations to the AdS background near the boundary. Specific examples include the ${cal N}=4$ SYM theory, and theories on D3 branes placed on orbifolds and conifolds. We also clarify some subtleties of the AdS/CFT correspondence that arise in this analysis. In particular, we explain how scalar fields in AdS space of sufficiently negative mass-squared can be associated with CFT operators of {it two} possible dimensions. All dimensions are bounded from below by $(d-2)/2$; this is the unitarity bound for scalar operators in $d$-dimensional field theory. We further argue that the generating functional for correlators in the theory with one choice of operator dimension is a Legendre transform of the generating functional in the theory with the other choice.
We consider duality between type 0B string theory on $AdS_5times S^5$ and the planar CFT on $N$ electric D3-branes coincident with $N$ magnetic D3-branes. It has been argued that this theory is stable up to a critical value of the `t Hooft coupling but is unstable beyond that point. We suggest that from the gauge theory point of view the development of instability is associated with singularity in the dimension of the operator corresponding to the tachyon field via the AdS/CFT map. Such singularities are common in large $N$ theories because summation over planar graphs typically has a finite radius of convergence. Hence we expect transitions between stability and instability for string theories in AdS backgrounds that are dual to certain large $N$ gauge theories: if there are tachyons for large AdS radius then they may be stabilized by reducing the radius below a critical value of order the string scale.
The non-renormalization of the 3-point functions $tr X^{k_1} tr X^{k_2} tr X^{k_3}$ of chiral primary operators in N=4 super-Yang-Mills theory is one of the most striking facts to emerge from the AdS/CFT correspondence. A two-fold puzzle appears in the extremal case, e.g. k_1 = k_2 + k_3. First, the supergravity calculation involves analytic continuation in the k_i variables to define the product of a vanishing bulk coupling and an infinite integral over AdS. Second, extremal correlators are uniquely sensitive to mixing of the single-trace operators $tr X^k$ with protected multi-trace operators in the same representation of SU(4). We show that the calculation of extremal correlators from supergravity is subject to the same subtlety of regularization known for the 2-point functions, and we present a careful method which justifies the analytic continuation and shows that supergravity fields couple to single traces without admixture. We also study extremal n-point functions of chiral primary operators, and argue that Type IIB supergravity requires that their space-time form is a product of n-1 two-point functions (as in the free field approximation) multiplied by a non-renormalized coefficient. This non-renormalization property of extremal n-point functions is a new prediction of the AdS/CFT correspondence. As a byproduct of this work we obtain the cubic couplings $t phi phi$ and $s phi phi$ of fields in the dilaton and 5-sphere graviton towers of Type IIB supergravity on $AdS_5 times S^5$.
The AdS-CFT correspondence is established as a re-assignment of localization to the observables which is consistent with locality and covariance.
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