Dynamical Soft-Wall AdS/QCD

We present a solution of the five-dimensional gravity-dilaton-tachyon equations of motion with a pure AdS5 metric and a quadratic dilaton and linear tachyon in conformal coordinates. This leads to an infrared soft wall model where the dilaton profile gives rise to linear Regge trajectories for the four-dimensional mass spectrum of the dual gauge theory. Even though our approach is phenomenological the scalar fields resemble the dilaton and the closed string tachyon of a non-critical string theory. Interestingly, the linear tachyon has the correct profile to imply that chiral symmetry is not restored for highly excited states. Our solution thus provides a dynamical bottom-up model of linear confinement in holographic QCD. E-mail: [email protected] E-mail: [email protected] Address after January 2008: School of Physics, The University of Melbourne, Victoria 3010, Australia. The last decade has seen a renaissance in the study of gauge theories in the nonperturbative regime, spurred by the fascinating idea of gauge/string duality. Inspired by the anti-de Sitter/conformal field theory (AdS/CFT) correspondence [1, 2, 3], the basic tenet is that strongly coupled gauge theories can be equivalently described by higher-dimensional gravitational theories. The most obvious application of these ideas is to model Quantum Chromodynamics (QCD), the theory of strong interactions describing the low energy hadrons of our world. A bottom-up approach to these studies known as AdS/ QCD uses the basic features of QCD to gain an understanding of the hypothetical dual gravitational theory [4, 5]. In AdS/QCD models, one starts from a weakly coupled five-dimensional (5D) anti-de Sitter background, dual to conformal symmetry of the 4D field theory. This is a reasonable starting point since, due to asymptotic freedom, QCD is approximately conformal at high energies. Bulk fields are added to the 5D theory, which map to QCD operators through the AdS/CFT correspondence. Confinement is implemented either through a hard cutoff in the extra dimension, or by a dynamical cutoff, such as a nontrivial dilaton background [6, 7]. The lowest lying meson spectra and decay constants can be modeled quite well with these constructions. However, the main drawback thus far lies in the difficulty of constructing a dynamical model of confinement which produces the correct asymptotic linear Regge trajectories associated with higher radial or spin quantum numbers, as is expected both from the experimental data [8] and semiclassical QCD arguments [9]. In Ref. [10], a heuristic model was proposed in which confinement was modeled with a nontrivial dilaton background, quadratic in the conformal coordinate z. This so-called soft wall correctly produces the linear spectrum in both radial and spin directions. In the simplest model, the mesons follow a mass spectrum mn,S ∝ n + S for excitation number n and spin S (see also [11]). A similar proposal has been put forth which modifies the metric in the infrared (IR) at large z [12]. To date, however, a dynamical model of these setups has not been found. In this work, we present a dynamical soft-wall model with a pure AdS metric and quadratic in z “dilaton” Φ. Our setup requires an additional scalar field, a “tachyon” T . Although it is not immediately obvious how to embed our model into string theory, certain features of the scalar potential suggest that Φ and T may be identified with the dilaton and the closed string tachyon of a non-critical string theory. At the same time, other aspects of the scalar potential appear rather exotic, as we will discuss further. Nevertheless, our solution is, at a minimum, a phenomenological bottom-up holographic model of linear confinement and dynamical realization of the proposals in [10] and [12], and may yield further insight into the nature of the string theory dual to QCD. We note that an alternative mechanism achieving linear confinement, which relies on open string tachyon condensation, has recently been suggested in [13]. We will assume that four-dimensional (4D) QCD with a large number of colors