Exploring improved holographic theories for QCD: Part II

TL;DR

The paper develops a bottom-up 5D holographic QCD framework based on Einstein–Dilaton gravity to model large-N_c QCD with UV asymptotic freedom and IR confinement. By classifying IR-confining geometries and leveraging a superpotential/beta-function dictionary, it connects Wilson-loop confinement to IR geometry, shows the existence of a mass gap and a discrete glueball spectrum, and derives universal large-n mass ratios. The analysis includes axion dynamics and theta-angle screening, and introduces flavor through tachyon condensation to obtain chiral symmetry breaking and vector mesons. Concrete backgrounds are constructed (one with unbounded conformal coordinate and another with a finite IR singularity), and glueball spectra are computed and compared with lattice data, highlighting strengths (linear Regge-like behavior for certain backgrounds) and limitations (difficulty fitting multiple sectors simultaneously in finite-r0 backgrounds). Overall, the work advances a consistent holographic description of confinement and nonperturbative YM dynamics, offering quantitative glueball predictions and insights into CP-violation screening and meson spectra within a controlled large-N_c framework.

Abstract

This paper is a continuation of ArXiv:0707.1324 where improved holographic theories for QCD were set up and explored. Here, the IR confining geometries are classified and analyzed. They all end in a "good" (repulsive) singularity in the IR. The glueball spectra are gaped and discrete, and they favorably compare to the lattice data. Quite generally, confinement and discrete spectra imply each other. Asymptotically linear glueball masses can also be achieved. Asymptotic mass ratios of various glueballs with different spin also turn out to be universal. Mesons dynamics is implemented via space filling D4-anti-D4 brane pairs. The associated tachyon dynamics is analyzed and chiral symmetry breaking is shown. The dynamics of the RR axion is analyzed, and the non-perturbative running of the QCD theta-angle is obtained. It is shown to always vanish in the IR.

Figures (14)

• Figure 1: An example of the axion profile (normalized to one in the UV) as a function of energy, in one of the explicit cases we treat numerically in Section \ref{['numerics']}. The energy scale is in MeV, and it is normalized to match the mass of the lowest scalar glueball from lattice data, $m_0=1475 MeV$. The axion kinetic function is taken as $Z(\lambda) =Z_a( 1 + c_a \lambda^{4})$, with $c_a=100$ while it does not depend on the value of $Z_a$. The vertical dashed line corresponds to $\Lambda_{QCD}$ as defined in eq. (\ref{['l2l2']}). In this particular case $\Lambda = 290 MeV$.
• Figure 2: A detail showing the different axion profiles for different values of $c_a$. The values are $c_a=0.1$ (dashed line), $c_a=10$ (dotted line) and $c_a=100$ (solid line).
• Figure 3: The profile of the scale factor and the dilaton in a typical solution. $u_*$ is the curvature singularity where the scale factor shrinks to zero and the dilaton blows up.
• Figure 4: The scale factor and 't Hooft coupling that follow from (\ref{['xexact']}), $b_0=4.2$, and initial conditions $A_0=0$, $\lambda_0=0.05$ at $r=0.36$. The units are such that $\ell=1$. The dashed line represents the scale factor for pure $AdS$.
• Figure 6: Effective Schrödinger potentials for scalar (solid line) and tensor (dashed line) glueballs. The units are chosen such that $\ell=1$.