Asymptotic Freedom and Dirichlet String Theory, UR-1288, ER-40685-737

TL;DR

This paper demonstrates that Dirichlet string theory exhibits logarithmic energy dependence in fixed angle scattering and temperature, suggesting a potential link between string behavior and asymptotic freedom in QCD.

Contribution

It introduces the logarithmic energy dependence in Dirichlet string theory scattering and thermodynamics, offering insights into connecting string theory with asymptotic freedom.

Findings

Logarithmic dependence of scattering amplitude on energy.

Logarithmic dependence of free energy on temperature.

Potential mechanism linking string theory to QCD asymptotic freedom.

Abstract

Fixed angle scattering at high energy in a string theory with boundaries satisfying Dirichlet conditions (Dirichlet strings) in $D=4$ is shown to have logarithmic dependence on energy, in addition to the power-like behavior known before. High temperature free energy also depends logarithmically on temperature. Such a result could provide a matching mechanism between strings at long distance and asymptotic freedom at short distance, which is necessary for the reformulation of large-$N$ QCD as a string theory.