Springer Berlin Heidelberg
Berlin/Heidelberg
Springer
13130
10.1007/13130.1029-8479
1029-8479
32745009
Journal of High Energy Physics
J. High Energ. Phys.
Physics
Elementary Particles, Quantum Field Theory
Quantum Field Theories, String Theory
Classical and Quantum Gravitation, Relativity Theory
Quantum Physics
Physics and Astronomy
2018
2018
12
11
11
93
2018
11
SISSA, Trieste, Italy
2018
9399
1806.10894
10.1007/JHEP11(2018)092
92
92
Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
Regular Article - Theoretical Physics
1
36
2018
11
14
2018
9
12
2018
10
30
2018
11
14
The Author(s)
2018
13130
2018
2018
11
11
Georg
Bergner
georg.bergner@uni-jena.de
Stefano
Piemonte
stefano.piemonte@ur.de
Mithat
Ünsal
unsal.mithat@gmail.com
0000 0001 1939 2794
grid.9613.d
Friedrich-Schiller-University Jena, Institute of Theoretical Physics
Max-Wien-Platz 1
D-07743
Jena
Germany
0000 0001 2190 5763
grid.7727.5
University of Regensburg, Institute for Theoretical Physics
Universitätsstr. 31
D-93040
Regensburg
Germany
0000 0001 2173 6074
grid.40803.3f
Department of Physics
North Carolina State University
Raleigh
NC
27695
U.S.A.
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 × 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
$\mathcal{N}=1$
$$ \mathcal{N}=1 $$
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
$\mathcal{N}=1$
$$ \mathcal{N}=1 $$
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.
Keywords
Confinement
Lattice Quantum Field Theory
Supersymmetric Gauge Theory
Wilson, ’t Hooft and Polyakov loops
ArXiv ePrint:
1806.10894