Geometric aspects of confining strings

Confining strings in 4D are effective, thick strings describing the confinement phase of compact U(1) and, possibly, also non-Abelian gauge fields. We show that these strings are dual to the gauge fields, inasmuch their perturbative regime corresponds to the strong coupling (e >> 1) regime of the gauge theory. In this regime they describe smooth surfaces with long-range correlations and Hausdorff dimension two. For lower couplings e and monopole fugacities z, a phase transition takes place, beyond which the smooth string picture is lost. On the critical line intrinsic distances on the surface diverge and correlators vanish, indicating that world-sheets become fractal. (C) 1998 Elsevier Science B.V.