Building a “holographic dual” to QCD in the AdS5: instantons and confinement

Recent attempts to find a “holographic dual” to QCD-like theories included a suggestion by Karsh et al (below referred to as KKSS) to incorporate confinement via a potential quadratically increasing into the 5-th direction of the AdS5 space. We show that the same conclusion follows from completely different line of arguments. If instantons are promoted into the 5d space by identifying the instanton size ρ at the 5-th coordinate, the background geometry necessarily should be the AdS5. As I argued already in 1999, confinement described via “dual superconductivity” leads to a factor exp(−2πσρ2), where σ is a string tension, which is nearly exactly identical to that suggested by KKSS. This expression is also well supported by available lattice data. At the end of the paper we propose a IR potential generalized to the nonzero temperatures. 1.AdS/CFT correspondence is a conjectured duality between the conformal N=4 supersymmetric Yang-Mills theory in d=4 dimensions (to be called CFT for short below) and the string theory in AdS5 × O5, which passed an impressive number of particular tests (see review [1]). It is clearly the most interesting development at the interface of string/field theory. It is