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## 4.2.2 Glueballs 

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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: 

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. 

## 4.3 Chiral Symmetry Breaking 

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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, 

