Gauge/Gravity Correspondence and QCD

String theory has experienced a revolutionary period since around 1995. One of the most important discovery is the D-brane. It has opened up profound relationship between string theory and quantum field theory. Now we have come to the stage to consider realistic physics by applying the techniques developed in string theory to QCD. The purpose of this note is to provide a brief overview on the application of the string theory to QCD, mainly based on Ref. 1). Let us begin by explaining what D-branes are. D-branes are extended objects living in the ten dimensional space-time of superstring theory. A Dp-brane is defined as (p + 1)-dimensional manifold on which the end points of open strings can be attached. A crucial fact is that there is a massless gauge field in the open string spectrum. If we consider Nc D-branes located at the same place, each of the two end points of each open string carries an index a = 1, · · · , Nc (Chan-Paton index) that labels which D-brane the end point is attached. In this case, the gauge field carries two indices and hence it is considered as an Nc × Nc matrix. In fact, it is interpreted as a U(Nc) gauge field. Therefore, we can realize (p + 1)-dimensional U(Nc) gauge theory on the Dp-brane. This is the basic idea to construct non-abelian gauge theories in string theory. We can apply this construction to more complicated brane configurations to realize various gauge theories.