Confinement of N=1 Super Yang-Mills from Supergravity

TL;DR

This paper demonstrates confinement and asymptotic freedom in N=1 super Yang-Mills by calculating Wilson loops using supergravity duals, revealing area law at large distances and logarithmic behavior at short distances.

Contribution

It provides a numerical calculation of Wilson loops in N=1 super Yang-Mills from supergravity, confirming confinement and asymptotic freedom within the gauge/gravity duality framework.

Findings

Wilson loop shows area law at large radius indicating confinement.

Wilson loop exhibits logarithmic behavior at small radius indicating asymptotic freedom.

Numerical methods used to connect supergravity solutions with gauge theory phenomena.

Abstract

We calculate circular Wilson loop expectation value of pure ${\cal N}=1$ super Yang-Mills from the Klebanov-Strassker-Tseytlin solution of supergravity and the proposed gauge/gravity duality. The calculation is performed numerically via searching world-sheet minimal surface. It is shown that Wilson loop exhibits area law for large radius which implies that ${\cal N}=1$ super Yang-Mills is confined at large distance or low energy scale. Meanwhile, Wilson loop exhibits logarithmic behavior for small radius and it indicates asymptotical freedom of ${\cal N}=1$ super Yang-Mills at short distance or high energy scale.