content_image/324729.jpg
a Goldstone boson though, because of the presence of instantons. However, in the ’t Hooft limit ( N −→ ∞ with g 2 $_{YM}$N fixed), the instanton effect is negated, and so the Goldstone boson becomes light once again. 

## 3.2 Particle spectrum in the probe limit 

The excitations of the D7-brane in the directions perpendicular to its world volume correspond to scalar fields, which are singlets under the colour group and are in the adjoint of the flavour group: these states include mesons. 

Since the theory is supersymmetric, there will also be other states, in- cluding fermions, living on the brane, but these are not explored in this thesis. 

The presence of supersymmetry also means that a fermion condensate cannot be expected to form (we check this explicitly in the next section). Hence chiral symmetry will not be spontaneously broken, as it is in QCD. Non-supersymmetric deformations of the correspondence can overcome this drawback, and in chapter 4 we address a particularly important example of such a deformation. 

## 3.2.1 Quark mass and condensate 

In this section we analyse how the probe D7 brane lies when introduced into the D3-brane setup. We will show that its asymptotic solution is holographic to the quark mass and condensate. 

The full action for a probe D7-brane in the D3-brane setup is 

<img src='content_image/324729.jpg'>

where G is the ten dimensional metric, and F is the field strength of the 

