Chapter 7 Improving the UV of Holographic Descriptions of QCD This thesis has investigated the possibility of finding a holographic descrip- tion of QCD. However, QCD is asymptotically free and thus its dual is strongly coupled in the UV. We don’t know how to solve string theory in the strongly coupled regime, and so a naive step is to simply eliminate this part of the duality by cutting off the gravity dual in the UV at some as yet undetermined energy Λ. The dual field theory is then only defined upto Λ. In this chapter we investigate the effect of including such a sharp UV cutoff in the gravity dual. The first task is to identify operator-field matches at r = Λ rather than at r = ∞ , which we discuss next. 97