The Hadronic Spectrum of a Holographic Dual of QCD

Abstract

We compute the spectrum of light hadrons in a holographic dual of QCD defined on AdS5 × S5 which has conformal behavior at short distances and confinement at large interquark separation. Specific hadrons are identified by the correspondence of string modes with the dimension of the interpolating operator of the hadron’s valence Fock state. Higher orbital excitations are matched quanta to quanta with fluctuations about the AdS background. Since only one parameter, the QCD scale ΛQCD, is used, the agreement with the pattern of physical states is remarkable. In particular, the ratio of Delta to nucleon trajectories is determined by the ratio of zeroes of Bessel functions. Work supported in part by the Department of Energy Contract DE-AC02-76SF00515 The correspondence [1] between 10-dimensional string theory defined on AdS5 × S and Yang-Mills theories at its conformal 3+1 space-time boundary [2] has led to important insights into the properties of QCD at strong coupling. As shown by Polchinski and Strassler [3], one can give a nonperturbative derivation of dimensional counting rules [4] for the leading power-law fall-off of hard exclusive glueball scattering in gauge theories with a mass gap dual to supergravity in warped space-times. The resulting theories have the hard behavior expected from QCD at short distances, rather than the soft behavior characteristic of string theory. Other important applications to hadron physics are the description of form factors at large transverse momentum [5] and the behavior of deep inelastic scattering structure functions at small x [6]. One can also derive the fall-off of hadronic light-front wavefunctions in QCD at large transverse momentum by matching their short-distance properties to the behavior of the string solutions in the large-r conformal region of AdS space [7]. The scale dependence of the string modes as one approaches the boundary from the interior of AdS space determines the analytic behavior of the QCD hadronic wavefunction, providing a precise counting rule for each Fock component with any number of quarks and gluons and any internal orbital angular momentum. The specific correspondence in the k⊥ → ∞ and x→ 1 limits provides a prescription which maps string modes into boundary states with well defined number of partons [7]. The predicted orbital dependence coincides with perturbative QCD analyses [8]. The AdS/CFT derivations validate QCD perturbative results [9, 10] and also confirm the dominance of the quark interchange mechanism [11] for exclusive QCD processes at large NC . Scaling laws and other aspects of high-energy scattering in warped backgrounds have also been addressed in [12]. The N = 4 super Yang-Mills (SYM) theory at large NC in four dimensions is dual to the low energy supergravity approximation to type IIB string compactified on AdS5 × S [1]. However, QCD is fundamentally different from SYM theories where all of the matter fields appear in adjoint multiplets of SU(NC). The introduction of quarks in the fundamental representation is dual to the introduction of an open string sector [13], where the strings end on a brane and join together at a point inside AdS space. In the procedure introduced by Karch and Katz [14], the endpoints of open strings are supported by Nf additional D7branes located along 1, 2, . . . , 7 dimensions. This system of NC D3-branes and Nf D7-branes leads to a a calculable meson spectrum [15]. QCD is a nearly conformal theory in the ultraviolet region and a confining gauge theory

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Cite this paper

@inproceedings{Tramond2005TheHS, title={The Hadronic Spectrum of a Holographic Dual of QCD}, author={Guy F. de T{\'e}ramond and Stanley J . Brodsky}, year={2005} }