Confining strings, Wilson loops and extra dimensions

TL;DR

This paper investigates how extra dimensions influence confinement phenomena in string theory by analyzing Wilson loops within a RG framework, revealing the dependence of confinement properties on a scale parameter related to these dimensions.

Contribution

It provides a detailed analysis of the effects of 21 extra dimensions on confinement and over-confinement in string theory using the RG approach and Wilson loop calculations.

Findings

Confinement and over-confinement depend on a scale l from extra dimensions.

The effective string tension varies with the scale l.

The confining range of couplings is explicitly calculated as a function of l.

Abstract

We study solutions of the one-loop beta-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 a four dimensional Minkowski spacetime times R and a 21-dimensional hyper-plane. In calculating the Wilson loops, as it is wellknown for this kind of confining geometry, two phenomena appear: confinement and over-confinement. 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 beta-function with an infrared attractive point (as the Novikov-Shifman-Vainshtein-Zakharov beta-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.