Large N QCD from Rotating Branes

TL;DR

This work presents a holographic approach to large-$N$ Yang–Mills in 3+1 and 2+1 dimensions using a one-parameter family of rotating D-brane supergravity backgrounds, controlled by the angular momentum parameter $a$. By tuning $a$, Kaluza–Klein modes from the compact D-brane directions decouple while ordinary glueball spectra remain stable, yielding mass ratios in good agreement with lattice results and improved alignment for certain states (notably $0^{-+}$) at large $a$. The authors also compute the finite-temperature free energy to extract the gluon condensate and, via RR-field dynamics, the topological susceptibility, finding universal scalings with the 't Hooft coupling $\lambda$, string tension $\sigma$, and color number $N$. Overall, the paper demonstrates a quantitative, tunable holographic avenue to study non-supersymmetric YM theories, with predictions matching lattice trends and revealing insights into KK decoupling and topological properties.

Abstract

We study large N SU(N) Yang-Mills theory in three and four dimensions using a one-parameter family of supergravity models which originate from non-extremal rotating D-branes. We show explicitly that varying this "angular momentum" parameter decouples the Kaluza-Klein modes associated with the compact D-brane coordinate, while the mass ratios for ordinary glueballs are quite stable against this variation, and are in good agreement with the latest lattice results. We also compute the topological susceptibility and the gluon condensate as a function of the "angular momentum" parameter.

Figures (8)

• Figure 2.1: The dependence of the ratio $r=\frac{M_{0^{++*}}}{M_{0^{++}}}$ of the masses of the first excited ($0^{++*}$) glueball state to the lowest $0^{++}$ glueball state on the parameter $a$ (in units where $u_0=1$). The ratio changes very little and takes on its asymptotic value quickly.
• Figure 2.2: The dependence of the ratio $r=\frac{M_{0^{-+}}}{M_{0^{++}}}$ on the parameter $a$ (in units where $u_0=1$). The change in the ratio is stable against the variation of $a$, however it increases by about 25% while going to $a=\infty$. The change is in agreement with lattice simulations. As explained in the text, this figure is reliable only for the regions $a \ll u_0$ or $a \gg u_0$ which are shown in the plot with a solid line, while for the intermediate region denoted by a dashed line there are corrections due to the non-vanishing off-diagonal component of the metric $g_{\theta_2 \varphi}$.
• Figure 2.3: The dependence of the ratio $r=\frac{M_{0^{++}}}{M_{KK}}$ of the the lowest $0^{++}$ glueball state compared to the KK mode wrapping the $\theta_2$ circle on the parameter $a$ in units where $u_0=1$. This KK mode decouples very quickly from the spectrum even in the supergravity approximation.
• Figure 2.4: The dependence of the ratio $r=\frac{M_{KK}}{M_{0^{++}}}$ of KK modes (corresponding to spherical harmonics with $l=1$ on $S^4$) compared to the lowest $0^{++}$ glueball state on the parameter $a$ in units where $u_0=1$. This KK mode does not decouple from the spectrum in the supergravity approximation even in the $a\to \infty$ limit.
• Figure 3.1: The dependence on $a$ of the ratio $r=\frac{M_{0^{++*}}}{M_{0^{++}}}$ in QCD$_3$. One can see that the ratio is very stable to changes in $a$, and reaches its asymptotic value quickly. $a$ is given in units of $u_0$.