Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice

TL;DR

This paper explores the non-perturbative phenomena of confinement and chiral symmetry breaking in lattice supersymmetric Yang-Mills theory, providing numerical evidence for phase stability and insights into abelian versus non-abelian confinement mechanisms.

Contribution

It presents the first lattice investigation of N=1 super Yang-Mills with evidence supporting the stability of center symmetry and suppression of chiral transitions at small compactification radii.

Findings

Numerical evidence for the absence of phase transitions with periodic boundary conditions at light fermion masses.

Suppression of chiral symmetry breaking transition in the studied regime.

Diagnostic method for distinguishing abelian from non-abelian confinement based on Polyakov loop eigenvalues.

Abstract

This work is a step towards merging the ideas that arise from semi-classical methods in continuum QFT with analytic/numerical lattice field theory. In this context, we consider Yang-Mills theories coupled to fermions in the adjoint representation. These theories have the remarkable property that confinement and discrete chiral symmetry breaking can persist at weak coupling on small (non-thermal) $\mathbb R^3 \times S^1$. This work presents a lattice investigation of Yang-Mills with one adjoint Majorana fermion, $\mathcal N=1$ super Yang-Mills, and opens the prospect to understand a number of non-perturbative phenomena, such as the mechanism of confinement, mass gap, chiral and center symmetry realizations both in lattice and continuum analytically. We study the compactification of this theory on the lattice with periodic and thermal boundary conditions. We provide numerical evidence for the conjectured absence of the phase transitions with periodic boundary conditions for sufficiently light lattice fermions (stability of center-symmetry), suppression of the chiral transition, and also provide a diagnostic for abelian vs. non-abelian confinement, based on per-site Polyakov loop eigenvalue distribution functions. In numerical and perturbative investigations we identify the role of the lattice artefacts that become relevant in the very small radius regime, and resolve some puzzles in the naive comparison between continuum and lattice.