2018/06/28 by Georg Bergner, Stefano Piemonte, Mithat Ünsal
Physics and Astronomy · #Black Holes and Theoretical Physics #Chiral symmetry breaking #Compactification (mathematics) #Fermion #Gauge theory #Hamiltonian lattice gauge theory #Lattice (music) #Lattice field theory #Lattice gauge theory #Lattice model (finance) #Orbifold #Quantum Chromodynamics and Particle Interactions #Topological Materials and Phenomena #hep-lat #hep-th
paper · pdf · doi:10.1007/jhep11(2018)092
38 pages, 12 figures
arxiv created 2018/06/28 · openalex created_date 2018/07/10 · openalex publication_date 2018/11/01 · arxiv updated 2018/12/05 · openalex updated_date 2026/08/05
A bstract 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 ℝ 3 × S 1 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 N=1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> 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 N=1 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> 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.