Dynamical AdS/Yang-Mills model

The $\mathrm{AdS}/\mathrm{CFT}$ correspondence has provided new and useful insights into the nonperturbative regime of strongly coupled gauge theories. We construct a class of models meant to mimic Yang-Mills theory using the superpotential method. This method allows us to efficiently address the problem of solving all the equations of motion. The conformal symmetry is broken in the infrared by a dilaton field. Using a five-dimensional action, we calculate the mass spectrum of scalar glueballs. This spectrum contains a tachyon, indicating an instability in the theory. We stabilize the theory by introducing a cosmological constant in the bulk and a pair of 3-branes, as in the Randall-Sundrum model. The scalar glueball masses computed by lattice gauge theory are then described very well by just a few parameters. Prospects for extending the model to other spins and parities and to finite temperature are considered.

Figure 1

The scalar glueball mass spectrum as computed on the lattice in pure SU(3) gauge theory. The linear fit includes $n\ge 2$.

Figure 2

The scalar glueball mass spectrum as computed on the lattice in pure SU(3) gauge theory. The linear fit includes $n\ge 1$.

Figure 3

The glueball field as a function of the dimensionless variable $\sqrt{\lambda }z$. Plotted this way, it only depends on the parameter $\gamma$, which here is chosen to be $1/2$.

Figure 4

The dilaton field as a function of the dimensionless variable $\sqrt{\lambda }z$. Plotted this way, it only depends on the parameter $\gamma$, which here is chosen to be $1/2$.

Figure 5

The mass spectra with $\sqrt{\lambda }=700\mathrm{MeV}$ for several values of the parameter $\gamma$.

Figure 6

Glueball mass spectrum calculated with the $\mathrm{AdS}/\mathrm{YM}$ model including the Randall-Sundrum 3-brane. The best-fit parameters are given in the text.

Figure 7

The Schrödinger potential for the $\mathrm{AdS}/\mathrm{YM}$ model including the Randall-Sundrum 3-brane.