Glueballs vs. Gluinoballs: Fluctuation Spectra in Non-AdS/Non-CFT

TL;DR

The paper investigates mass spectra for non-AdS/Non-CFT holographic duals, focusing on MN and KS backgrounds. It introduces a determinant-based method to extract spin-0 and spin-2 bulk fluctuation spectra from a 5D sigma-model with a fake supergravity potential, avoiding hard-wall IR cutoffs. The KS system exhibits towers of states with quadratic confinement, $m^2 \sim a n^2$ with $a \approx 0.2715$, including seven nearly degenerate towers, while MN yields an upper-bounded discrete spectrum; hard-wall approximations fail to capture these features. Together, these results demonstrate a robust approach to holographic spectra in confining theories and highlight the crucial role of IR dynamics in determining low-lying states, offering guidance for modeling confinement in holographic QCD and related theories.

Abstract

Building on earlier results on holographic bulk dynamics in confining gauge theories, we compute the spin-0 and spin-2 spectra of gauge theories dual to the non-singular Maldacena-Nunez and Klebanov-Strassler supergravity backgrounds. We construct and apply a numerical recipe for computing mass spectra from certain determinants. In the Klebanov-Strassler case, states containing the glueball and gluinoball obey "quadratic confinement", i.e. their mass-squareds depend on consecutive number as m^2 ~ n^2 for large n, with a universal proportionality constant. The hardwall approximation appears to work poorly when compared to the unique spectra we find in the full theory with a smooth cap-off in the infrared.

Figures (6)

• Figure 1: Warp factors $h(r)$. The string tension goes like $h^{-1/2}$. From left to right the figures show the form of the warp factor in AdS (tension goes to zero in infrared), Klebanov-Tseytlin (tension diverges at $r_{\rm s}$) and Klebanov-Strassler (tension goes to finite value).
• Figure 2: The function \ref{['MN:fmn']} for the numerical mass spectrum in the MN background.
• Figure 3: Mass-squared values of spin-2 states. The solid line represents the fit \ref{['KS:spin2fit']}.
• Figure 4: $\det \gamma$ as a function of $k^2$. For clarity, we have taken the 14th root of the absolute value of the determinant (leaving its sign untouched). The plot shows clearly that there are no zero crossings for positive $k^2$. The inset shows the zeros of $\det \gamma$ for the first three spin-0 states.
• Figure 5: Here we plot $\det \gamma$ in the range $k^2 \in [-5.8 \ldots -5.3]$. The inset zooms in on the region around $k^2=-5.63$, where there are two zeros.