Glueball Spectrum for QCD from AdS Supergravity Duality

TL;DR

This work computes the complete glueball spectrum of QCD-like theories in the strong coupling regime via the AdS/CFT correspondence, using an $AdS^7 \times S^4$ black hole to model QCD_4 and an $AdS^5 \times S^5$ black hole for QCD_3. It derives six independent wave equations from fluctuations of the supergravity fields, computes their discrete spectra, and assigns parity and charge conjugation by Born-Infeld couplings, yielding a rich pattern of $J^{PC}$ states. Despite the limitations of leading-order strong coupling, the resulting mass and spin structure show qualitative agreement with lattice QCD data, offering support for the Maldacena duality and insights into strong-coupling artifacts and operator mappings. The work also discusses the Pomeron intercept in the strong coupling regime and outlines how KK and other spurious modes decouple, guiding future refinements toward a more precise gauge/gravity dual for QCD.

Abstract

We present the analysis of the complete glueball spectrum for the $AdS^7$ black hole supergravity dual of $QCD_4$ in strong coupling limit: $g^2 N \to \infty$. The bosonic fields in the supergravity multiplet lead to 6 independent wave equations contributing to glueball states with $J^{PC} = 2^{++},1^{+-}, 1^{--}$, $0^{++}$ and $0^{-+}$. We study the spectral splitting and degeneracy patterns for both $QCD_4$ and $QCD_3$. Despite the expected limitations of a leading order strong coupling approximation, the pattern of spins, parities and mass inequalities bear a striking resemblance to the known $QCD_4$ glueball spectrum as determined by lattice simulations at weak coupling.

Figures (2)

• Figure 1: The AdS glueball spectrum for $QCD_4$ (left) and $QCD_3$ (right) with mass eigenvalues, $m_n$, plotted for each of the six equations labeled on the horizontal axis.
• Figure 2: The AdS glueball spectrum for $QCD_4$ in strong coupling (left) compared with the lattice spectrum MP for pure SU(3) QCD (right). The AdS cut-off scale is adjusted to set the lowest $2^{++}$ tensor state to the lattice results in units of the hadronic scale $1/r_0 = 410$ Mev.