Glueball State Mass 0 ++ 1.00 0 ++ ∗ 1.56 0 ++ ∗∗ 2.08 0 ++ ∗∗∗ 2.60 0 ++ ∗∗∗∗ 3.11 Table 4.1: 0 ++ glueball masses from Constable Myers geometry. Normal- ization is such that the ground state mass is set to one (arbitrary units). 4.2.2 Glueballs 4.3 Chiral Symmetry Breaking 64 The most exciting aspect of this geometry is that once we introduce quarks, a quark condensate forms spontaneously. This is an essential characteristic of QCD. We start by introducing quarks in the same way we did in chapter 3, with the metric given in equation (4.1). Making the ans¨ atz Φ = g ( ρ ) e ik.x (since the scalar field is assumed to be a small perturbation) we then look for solutions to (4.17). This can be done numerically. As r −→ ∞ , the metric asymptotes to AdS space, and the normalizable solution to the wave equation goes like r − $^{4}$. Hence we use the boundary conditions g (Λ) = Λ − $^{4}$, g ′ (Λ) = − 4Λ − 5 we then look for those solutions which obey f ′ (0) = 0 (for continuity). We find a discrete spectrum (table 4.1). In other words, this geometry has a mass gap in the glueball sector. The glueball spectrum for this geometry was investigated in [109]. The procedure for calculating holographic glueball spectra is quite straightfor- ward [82–84,112]: it is found by solving the equation of motion for the scalar field Φ: ∂$_{µ}$ ( √ gg µν $_{e}$− 2 $^{φ}$∂$_{ν}$ Φ ) = 0 (4.17)