Confining strings, Wilson loops and extra dimensions

Abstract

We study solutions of the one-loop β-functions of the critical bosonic string theory in the framework of the Renormalization Group (RG) approach to string theory, considering explicitly the effects of the 21 extra dimensions. In the RG approach the 26-dimensional manifold is given in terms of M 4×R 1× H 21 . In calculating the Wilson loops, as it is well known for this kind of confining geometry, two phenomena appear: confinement and overconfinement. There is a critical minimal surface below of which it leads to confinement only. The role of the extra dimensions is understood in terms of a dimensionless scale l provided by them. Therefore, the effective string tension in the area law, the length of the Wilson loops, as well as, the size of the critical minimal surface depend on this scale. When this confining geometry is used to study a field-theory β-function with an infrared attractive point (as the Novikov–Shifman–Vainshtein–Zakharov β-function) the range of the couplings where the field theory is confining depends on that scale. We have explicitly calculated the l-dependence of that range.