Spin-Two Glueballs, Positive Energy Theorems and the AdS/CFT Correspondence

TL;DR

This work computes the spectrum of spin-two graviton excitations in the AdS soliton background of $p+2$ dimensions and maps them, via AdS/CFT, to spin-two glueballs in the dual $p$-dimensional theories (notably QCD$_3$ and QCD$_4$ for $p=3$ and $5$). The authors show an exact degeneracy between tensor (spin-two) and certain scalar excitations across all $p$, deriving the spectra through a unified Schrödinger-form analysis and a WKB treatment. They also establish the perturbative stability of the AdS soliton by proving $M^2>0$ for all modes, extending the positive energy conjecture to arbitrary dimensions. The results highlight a striking strong-coupling prediction—tensor and scalar glueballs are degenerate—contrasting with current lattice findings at weaker coupling and inviting further study of higher-derivative corrections and decoupling mechanisms.

Abstract

We determine the spectrum of graviton excitations in the background geometry of the AdS soliton in p+2 dimensions. Via the AdS/CFT correspondence this corresponds to determining the spectrum of spin two excitations in the dual effective p-dimensional field theories For the cases of D3- and M5-branes these are the spin two glueballs of QCD_3 and QCD_4 respectively. For all values of p we find an exact degeneracy of the spectra of these tensor states and certain scalar excitations. Our results also extend the perturbative proof of a positive energy conjecture for asymptotically locally AdS spacetimes (originally proposed for p=3) to an arbritrary number of dimensions.

Figures (3)

• Figure 1: Plot of the effective potential $V(y)$ in eq. (\ref{['eq:pot']}) for $p=3$ and $\frac{M^2L^4}{R^2}=50$. The figure demonstrates the existence of two classical turning points.
• Figure 2: Plot of the effective potential $V(y)$ in eq. (\ref{['eq:eepot']}) for $p=3$ and $\frac{M^2L^4}{R^2}=50$. There are two classical turning points for finite values of $y$.
• Figure 3: Plot of the effective potential $V(y)$ in eq. (\ref{['eq:diagpot']}) for $p=3$ and $\frac{M^2L^4}{R^2}=50$. Note the similarity to fig. (\ref{['fig:ttpot']}).