Abstract
We advance in constructing a bottom-up holographic theory of linear meson Regge trajectories that generalizes and unites into one logical framework various bottom-up holographic approaches proposed in the past and scattered in the literature. The starting point of the theory is a quadratic in fields holographic five-dimensional action in which the Poincaré invariance along the holographic coordinate is violated in the most general way compatible with the linear Regge behavior of the discrete spectrum in four dimensions. It is further demonstrated how different Soft Wall (SW) like holographic models existing in the literature plus some new ones emerge from our general setup. Various interrelations between the emerging models are studied. These models include the known SW models with different sign in the exponential background, the SW models with certain generalized backgrounds, with modified metrics, and No Wall models with 5D mass depending on the holographic coordinate in a simple polynomial way. We argue that this dependence allows to describe the effects caused by the main non-local phenomena of strongly coupled 4D gauge theory, the confinement and chiral symmetry breaking, in terms of a local 5D dual field theory in the AdS space. We provide a detailed comparison of our approach with the Light Front holographic QCD, with the spectroscopic predictions of the dual Veneziano like amplitudes, and with the experimental Regge phenomenology. We apply our general approach to a holographic study of confinement, chiral symmetry breaking, and the pion form factor.
Highlights
C (2022) 82:195 includes various top-down holographic models which start from some brane construction within a string theory and try to get a dual model useful for the QCD phenomenology
This means, in particular, that the Soft Wall (SW) holographic models are closely related with the planar QCD sum rules which were widely used in the past to study the phenomenology of linear radial trajectories in the meson sector [70]
After that we demonstrate how various SW like holographic models existing in the literature plus some new ones emerge from our general setup and study interrelations between the emerging models
Summary
The spectrum of 4D modes of the model (2.1) is discrete and given by the relation (A.11) of Appendix A for spin J = 0, m2n = 2|c| 2n + 1 + 4 + m25 R2 − |cc| , n = 0, 1, 2, This spectrum has a Regge form due to the dilaton background ecz in the 5D action (2.1). It should be noted that if the higher spin fields are described as pure gauge 5D fields, when the relation (2.8) near the UV boundary is not imposed, the situation is opposite – the simplest solution, a1 = a2 = b = 0, c = −λ2, is achieved when c < 0 This description was exploited in the original paper where the SW holographic model was introduced [60]. It is not surprising that the agreement with the data presented in Ref. [73] looked impressive
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