much sense, so b must be greater than or equal to 40 − 1 / $^{8}$R . Below this, the geometry is not well-defined. 

Meanwhile R determines g 2 $_{YM}$N in the field theory, as is usual in the correspondence. So R specifies if the field theory is in the strongly coupled or weakly coupled regime. 

## 4.2 Confinement and Glueballs in the Constable- Myers Geometry 

Before we introduce quarks into this geometry, it is worth pausing to con- sider some of the properties already present in this theory, namely confine- ment and the glueball spectrum. 

## 4.2.1 Confinement 

Confinement means that quarks are consigned to exist in colour-neutral combinations. A single quark cannot exist on its own. One way of showing this is to calculate the energy of a quark-antiquark as a function of their separation. In QED, the energy between a positron-electron pair would monotonically decrease to zero as we separated the two. In QCD, we’d expect the energy to increase as we tried to separate a quark-antiquark pair, showing that it would take an infinite amount of energy to produce a solitary quark. 

In [110] it is argued that this effect can be studied holographically by looking at the Nambu-Goto action for a fundamental string in the geometry dual to the field theory. Specifically, the expectation value of a Wilson loop in the field theory is dual to the fundamental string in the holographic background: 

