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 transforming in the adjoint representation of the gauge group. These theories have the remarkable property that confinement and discrete chiral symmetry breaking can persist at weak coupling on ℝ3 × S1 up to small (non-thermal) compactification radii. This work presents a lattice investigation of a gauge theory coupled to a single adjoint Majorana fermion, the mathcal{N}=1 Supersymmetric Yang-Mills theory (SYM), and opens the prospect to understand analytically a number of non-perturbative phenomena, such as confinement, mass gap, chiral and center symmetry realizations, both on the lattice and in the continuum. We study the compactification of mathcal{N}=1 SYM on the lattice with periodic and thermal boundary conditions applied to the fermion field. We provide numerical evidences for the conjectured absence of phase transitions with periodic boundary conditions for sufficiently light lattice fermions (stability of center-symmetry), for the suppression of the chiral transition, and we provide also a diagnostic for Abelian vs. non-Abelian confinement, based on per-site Polyakov loop eigenvalue distribution functions. We identify the role of the lattice artefacts that become relevant in the very small radius regime, and we resolve some puzzles in the naive comparison between continuum and lattice.
Highlights
Mechanism, and the other is that in theories with exactly massless fermions, the Polyakov mechanism would not work [2]
This work presents a lattice investigation of a gauge theory coupled to a single adjoint Majorana fermion, the N = 1 Supersymmetric Yang-Mills theory (SYM), and opens the prospect to understand analytically a number of non-perturbative phenomena, such as confinement, mass gap, chiral and center symmetry realizations, both on the lattice and in the continuum
We provide numerical evidences for the conjectured absence of phase transitions with periodic boundary conditions for sufficiently light lattice fermions, for the suppression of the chiral transition, and we provide a diagnostic for Abelian vs. non-Abelian confinement, based on per-site Polyakov loop eigenvalue distribution functions
Summary
QCD(adj) consists of a non-Abelian gauge-field Acμ(x) minimally coupled to Nf Majorana fermions λci (x). In numerical simulations the lattice extend is finite in all directions. If fermions fields fulfill anti-periodic boundary conditions in the S1 direction, the theory on the T 3 × S1 torus emulates the thermal partition function of a quantum field theory in a box. If periodic boundary conditions are applied to fermion fields on S1 direction, the theory on T 3 × S1 corresponds to the twisted partition function (1.1) with no thermal interpretation. The latter setup is useful to realize the notion of adiabatic continuity. The continuum limit and the massless limit must be extrapolated from the numerical data
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