Abstract
Two-point current correlation functions of the large $N$ limit of supersymmetric and non-supersymmetric Yang-Mills theories at strong coupling are investigated in terms of their string theory dual models with quenched flavors. We consider non-Abelian global symmetry currents, which allow one to investigate vector mesons with $N_f > 1$. From the correlation functions we construct the deep inelastic scattering hadronic tensor of spin-one mesons, obtaining the corresponding eight structure functions for polarized vector mesons. We obtain several relations among the structure functions. Relations among some of their moments are also derived. Aspects of the sub-leading contributions in the $1/N$ and $N_f/N$ expansions are discussed. At leading order we find a universal behavior of the hadronic structure functions.
Highlights
For each holographic dual model we have found that the two-point correlation functions of non-Abelian (Nf > 1) global symmetry currents can generically be written as the product of a constant, which depends on the particular Dp-brane model, times flavor preserving Kronecker deltas multiplying the corresponding Abelian (Nf = 1) result for the same Dp-brane model
We have obtained a universal factorization of the two-point correlation functions for non-Abelian symmetry currents in a model-dependent factor times a modelindependent one
As we mentioned in the introduction we have performed a detailed analysis of the structure of the two-point correlation functions of generic global symmetry currents at strong coupling, associated with flavors in the fundamental representation of the gauge group, in the quenched approximation, in terms of the corresponding holographic string theory dual description
Summary
In what follows we adopt the conventions of Manohar [7], except for the Minkowski metric, which we define as being mostly plus. The four-momentum of the scattered lepton k′μ (with k′0 ≡ E′) is measured, but the final hadronic state called X is not. The lepton and the initial hadronic state exchange a virtual photon with four-momentum qμ. The hadronic tensor can be recast in terms of its structure functions. The so-called partonic distribution functions, which can be calculated from the structure functions, give the probability that a hadron contains a given constituent with a given fraction x of its total momentum. The structure functions are obtained from the most general Lorentz decomposition of the hadronic tensor Wμν, satisfying parity invariance, time reversal symmetry, and invariance under translations. Sμν, tμν, uμν and sσ, which depend on the hadron polarization, on the hadron and virtual photon momenta, and on the t and x variables, are defined in appendix A. Where Fj is the j-th structure function of the Tμν tensor, while Fj is the one corresponding to the Wμν tensor
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