Building a "holographic dual" to QCD in the AdS$_5$: instantons and confinement

TL;DR

This paper demonstrates that a holographic dual to QCD with confinement can be derived from instanton considerations, leading to an AdS$_5$ background and a potential consistent with lattice data and previous models.

Contribution

It shows that instanton-based arguments naturally lead to an AdS$_5$ background and confinement potential, aligning with prior holographic models and lattice results.

Findings

Instantons promote to 5D with instanton size as the 5th coordinate.

The background geometry must be AdS$_5$ for instantons to be consistent.

The confinement potential matches previous models and lattice data.

Abstract

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 $AdS_5$ 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 $\rho$ at the 5-th coordinate, the background geometry necessarily should be the AdS$_5$. As I argued already in 1999, confinement described via ``dual superconductivity'' leads to a factor $exp(-2\pi\sigma\rho^2)$, where $\sigma$ 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.