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

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.

arXiv comment38 pages, 12 figures

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• Notes on Confinement on ${\mathbf{R}}^3\times {\mathbf{S}}^1$: From Yang-Mills, super-Yang-Mills, and QCD(adj) to QCD(F)
• Fractional instanton of the SU($3$) gauge theory in weak coupling regime
• $\theta$-dependence and center symmetry in Yang-Mills theories
• Lattice studies of supersymmetric gauge theories
• Different faces of confinement
• Lattice simulations of a gauge theory with mixed adjoint-fundamental matter
• Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow
• Investigating the conformal behaviour of SU(2) with one adjoint Dirac flavor
• Monte-Carlo simulations of overlap Majorana fermions
• Spectrum of Trace Deformed Yang-Mills Theories
• Exploring gauge theories with adjoint matter on the lattice
• Confinement on ${\mathbb{R}}^3\times {\mathbb{S}}^1$ and Double-String Collapse
• Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD