Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
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DOI：
10.1007/jhep11(2018)092
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发表时间：
2018-06
影响因子：
5.4
通讯作者：
G. Bergner;S. Piemonte;M. Ünsal
中科院分区：
文献类型：
--
作者：
G. Bergner;S. Piemonte;M. Ünsal
这项工作是朝着将连续统量子理论中的半经典方法与解析/数值格子场理论相结合的方向迈出的一步。在此背景下，我们考虑了在规范群的伴随表示中耦合到费米子变换的杨-米尔斯理论。这些理论具有一个显著的性质，即在ℝ3×S 1上的弱耦合下，禁闭和离散手征对称破缺可以持续到小(非热)紧致半径。本文对与单个伴随Majorana费米子耦合的规范理论--超对称杨-米尔斯理论(SYM)进行了晶格研究，为在晶格上和连续介质中解析地理解一些非微扰现象，如禁闭、质量隙、手征和中心对称实现开辟了前景。在周期边界条件和热边界条件下，我们研究了晶格上SYM的紧致化问题。我们提供了足够轻的晶格费米子(中心对称性的稳定性)没有周期边界条件的相变猜想不存在的数值证据，以及手征相变的抑制，我们还提供了基于逐点Polyakov环本征值分布函数的阿贝尔禁闭与非阿贝尔禁闭的诊断。我们确定了晶格伪影在非常小的半径范围内的作用，并解决了在连续统和晶格之间天真的比较中的一些难题。
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, theSupersymmetric 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 ofSYM 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.