Compactified N=1 supersymmetric Yang-Mills theory on the lattice: Continuity and the disappearance of the deconfinement transition

TL;DR

This study investigates how boundary conditions and fermion mass affect the confinement-deconfinement transition in N=1 supersymmetric Yang-Mills theory on the lattice, providing evidence for a smooth continuity as the fermion mass approaches zero.

Contribution

It provides the first lattice simulation evidence supporting the predicted continuity of supersymmetric Yang-Mills theory during compactification, especially as fermion mass approaches zero.

Findings

Deconfinement region shrinks with decreasing fermion mass.

No deconfinement transition observed at smallest fermion masses.

Results support the continuity hypothesis in supersymmetric Yang-Mills theory.

Abstract

Fermion boundary conditions play a relevant role in revealing the confinement mechanism of N=1 supersymmetric Yang-Mills theory with one compactified space-time dimension. A deconfinement phase transition occurs for a sufficiently small compactification radius, equivalent to a high temperature in the thermal theory where antiperiodic fermion boundary conditions are applied. Periodic fermion boundary conditions, on the other hand, are related to the Witten index and confinement is expected to persist independently of the length of the compactified dimension. We study this aspect with lattice Monte Carlo simulations for different values of the fermion mass parameter that breaks supersymmetry softly. We find a deconfined region that shrinks when the fermion mass is lowered. Deconfinement takes place between two confined regions at large and small compactification radii, that would correspond to low and high temperatures in the thermal theory. At the smallest fermion masses we find no indication of a deconfinement transition. These results are a first signal for the predicted continuity in the compactification of supersymmetric Yang-Mills theory.