## Chapter 3 

## Flavouring the AdS$_{5}$ × S 5 

All the matter discussed in chapter 2 was in the adjoint representation of the SU(N) colour group. This is because both ends of the open strings start and end on the same type of brane - a D3-brane - and so are indistinguishable. All the Chan-Paton factors are in effect colour indices. Quarks have both colour and flavour indices, and are in the fundamental representation of the gauge group. So we need strings in our geometry which can take on these properties. A lot of work, by a lot of contributers, showed that this is achieved by introducing D7 branes [45,60–76]. In this section we summarise the salient points of their work. 

## 3.1 The D7-Brane Probe 

A brane is massive, and will distort the spacetime in which it is placed. At the moment this is an unwanted complication for us, so we shall use the probe limit, which means that we ignore the gravitational effects of the new brane. This approximation, known as the quenched approximation, holds if N$_{f}$ ≪ N$_{c}$ , where N$_{f}$ is the number of probe branes, and N$_{c}$ is the number of D3 branes. This approximation is the same as introducing a test charge in 

