Soft walls in dynamic $\mathrm{AdS}/\mathrm{QCD}$ and the technidilaton

Dynamic $\mathrm{AdS}/\mathrm{QCD}$ is a modification of $\mathrm{AdS}/\mathrm{QCD}$ that includes the running of the anomalous dimension of the $\overline{q}q$ quark bilinear and in which the generation of the constituent quark mass plays the role of an IR wall. The model allows one to move away smoothly from the controlled spectrum of the $\mathcal{N}=2$ super Yang-Mills theory of the D3/probe-D7 system to more QCD-like theories with chiral symmetry breaking. We investigate soft wall behavior in the model that gives Regge trajectories with $M_{n,s}^2\sim n,s$. To achieve these behaviors requires the quark’s constituent mass to fall peculiarly sharply in the IR so that meson physics is sensitive to renormalization group (RG) scales well below the quark’s on-shell mass. Including soft wall behavior in models of walking gauge dynamics breaks the near conformal symmetry which is present above the quark on-shell mass which can generate a large mass for the technidilaton like state. We conclude that the meson spectrum is rather sensitive to the IR decoupling.

Figure 1

The Schroedinger wells for the $\mathcal{N}=2$ model for $s=1$, 2, 3, 4 which give a spectrum $M^2=4(n+s)(n+s+1)$, and a plot of the Mass trajectories vs spin, $s$, for the excitation numbers $n=1$, 2, 3, 4, 5.

Figure 2

The Schroedinger wells for the dynamically generated mass model for $s=1$, 2, 3, 4 and a plot of the mass trajectories vs spin, $s$, for the excitation numbers $n=1$, 2, 3, 4, 5.

Figure 3

The Schroedinger wells for the soft wall model with $L$ given by (33) for $s=1$, 2, 3, 4 and a plot of the mass trajectories vs spin, $s$, for the excitation numbers $n=1$, 2, 3, 4, 5.

Figure 4

The function $L(\rho )$ which reproduces the soft wall behavior of [13] with a constant dilaton. Also shown are examples of the profiles for the $\mathcal{N}=2$ theory ($L=\text{constant}$) and for the dynamically generated mass example [$L=1/(1+{\rho }^2)$]. The line $L=\rho$ is also plotted to show where the on-mass shell condition is satisfied.

Figure 5

The Schroedinger wells for the soft wall model with $L$ given by (33) for $s=1$, 2, 3, 4 and a plot of the Mass trajectories vs spin, $s$, for the excitation numbers $n=1$, 2, 3, 4, 5.

Figure 6

A plot of the $\sigma$ meson mass in units of the $\rho$ meson mass against $N_f$ in dynamic $\mathrm{AdS}/\mathrm{QCD}$. The points that fall to zero at the chiral transition at $N_f=12$ are those computed where the action is cutoff at the on-shell mass of the quark so the theory is blind to the deep IR conformal symmetry breaking, whilst the points that asymptote to a nonzero value at $N_f=12$ are for the soft wall variant.