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

Author:

Bergner Georg,Piemonte Stefano,Ünsal Mithat

Abstract

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 $$ \mathcal{N}=1 $$ 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 $$ \mathcal{N}=1 $$ 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.

Publisher

Springer Science and Business Media LLC

Subject

Nuclear and High Energy Physics

Cited by 15 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Beta functions of 2D adjoint QCD;Physical Review D;2024-05-10

2. Identifying topological structures with adjoint mode filtering;Journal of High Energy Physics;2024-05-06

3. Exploring Gauge Theories with Adjoint Matter on the Lattice;Universe;2022-11-24

4. Lattice studies of supersymmetric gauge theories;The European Physical Journal Special Topics;2022-11-16

5. Graded Hilbert spaces, quantum distillation and connecting SQCD to QCD;Journal of High Energy Physics;2022-03

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