Studies on Polyakov and Nambu–Goto random surface path integrals on QCD(SU(∞)): Interquark potential and phenomenological scattering amplitudes

Abstract

We present new path integral studies on the Polyakov noncritical and Nambu–Goto critical string theories and their applications to [Formula: see text] interquark potential. We also evaluate the long distance asymptotic behavior of the interquark potential on the Nambu–Goto string theory with an extrinsic term in Polyakov’s string at [Formula: see text]. We also propose an alternative and a new view to covariant Polyakov’s string path integral with a fourth-order two-dimensional quantum gravity, is an effective stringy description for [Formula: see text] at the deep infrared region.