Supergravity Models for 3+1 Dimensional QCD

TL;DR

The paper constructs and analyzes a two-parameter family of holographic models for 3+1D large-N QCD using rotating M5-brane backgrounds. It computes the scalar glueball spectrum and a broad class of KK modes via both WKB and numerical methods, finding that glueball mass ratios are remarkably stable across most of the parameter space and that KK modes from the circle decouple at large angular momenta while those from S^4 do not. Comparisons with lattice data show good agreement except on a special line where the geometry approaches a near-degenerate horizon, signaling breakdown of the supergravity approximation. The results clarify decoupling properties of extra-dimensional modes in these holographic QCD models and suggest further study of the supersymmetric limit to understand potential protection of glueball masses across coupling regimes.

Abstract

The most general black M5-brane solution of eleven-dimensional supergravity (with a flat R^4 spacetime in the brane and a regular horizon) is characterized by charge, mass and two angular momenta. We use this metric to construct general dual models of large-N QCD (at strong coupling) that depend on two free parameters. The mass spectrum of scalar particles is determined analytically (in the WKB approximation) and numerically in the whole two-dimensional parameter space. We compare the mass spectrum with analogous results from lattice calculations, and find that the supergravity predictions are close to the lattice results everywhere on the two dimensional parameter space except along a special line. We also examine the mass spectrum of the supergravity Kaluza-Klein (KK) modes and find that the KK modes along the compact D-brane coordinate decouple from the spectrum for large angular momenta. There are however KK modes charged under a U(1)xU(1) global symmetry which do not decouple anywhere on the parameter space. General formulas for the string tension and action are also given.

Figures (11)

• Figure 3.1: The unnormalized values of the $0^{++}$ glueball mass (the lowest eigenvalues of Eq. (\ref{['ggbb']})) as a function of the two angular momenta. Note that this function is smooth everywhere except in the region $a_1=a_2\rightarrow\infty$.
• Figure 3.2: The ratio of the $0^{++*}$ mass to the $0^{++}$ mass along a generic direction, chosen here to be $a_1=2a_2=a$. Note, that the change in the ratio is tiny, and the asymptotic value of the ratio is the same as in Ref. CORT98 in the case of $a_1\rightarrow \infty$, $a_2=0$.
• Figure 3.3: The behavior of the ratio $r$ of the mass of the excited $0^{++*}$ glueball mass to the $0^{++}$ mass along the line $a_1=a_2$. Note, that along this direction the solutions behave very differently than anywhere else in the parameter space and depart significantly from the lattice results.
• Figure 3.4: The ratio of the lowest $0^{-+}$ mass to the lowest $0^{++}$ mass along a generic direction, chosen here to be $a_1=2a_2=a$. Note, that the ratio is very stable against the variations of the parameters. The actual change in the ratio is sizeable, and independent of the direction chosen in the $(a_1,a_2)$ parameter space (except the line $a_1=a_2$) and agrees with the ratio found in Ref. CORT98 for the case of $a_1 \rightarrow \infty$, $a_2=0$. As explained in the text, this figure is only reliable for the regions $a \ll u_0$ and $a \gg u_0$ which are shown by solid lines, while for the intermediate region denoted by a dashed line there are corrections due to the non-vanishing off-diagonal components of the metric.
• Figure 3.5: The behavior of the ratio $r$ of the mass of the lowest $0^{-+}$ glueball mass to the lowest $0^{++}$ mass along the line $a_1=a_2$. As explained in the text, this figure is only reliable for the regions $a \ll u_0$ and $a \gg u_0$ which are shown by solid lines.