论文标题
su（n）分数键盘和斐波那契序列
SU(N) fractional instantons and the Fibonacci sequence
论文作者
论文摘要
我们通过数值方法研究了$ \ mathbf {r} \ times \ times \ mathbf {t}^3 $带有分数拓扑费$ q = 1/n $的新$ su（n）$ self-Dual Instanton解决方案。 They are obtained on a box with twisted boundary conditions with a very particular choice of twist: both the number of colours and the 't Hooft $\mathbf{Z}_N$ fluxes piercing the box are taken within the Fibonacci sequence, i.e. $N=F_n$ (the $nth$ number in the series) and $|\vec m| = | \ vec {k} | = f_ {n-2} $。基于以前的作品，尤其是参考文献的各种论点。 \ cite {chamizo：2016msz}，表明这种选择避免了大型$ n $限制中的体积独立性的细分。这些解决方案与仪表理论的哈密顿式公式相关，在该理论中，它们代表真空到维卡姆隧道事件，提升了扰动理论中存在的电通量部门之间的脱落性。我们讨论了解决方案的较大$ n $缩放属性，并评估了各种规格不变的数量，例如动作密度或威尔逊和Polyakov Loop操作员。
We study, by means of numerical methods, new $SU(N)$ self-dual instanton solutions on $\mathbf{R}\times \mathbf{T}^3$ with fractional topological charge $Q=1/N$. They are obtained on a box with twisted boundary conditions with a very particular choice of twist: both the number of colours and the 't Hooft $\mathbf{Z}_N$ fluxes piercing the box are taken within the Fibonacci sequence, i.e. $N=F_n$ (the $nth$ number in the series) and $|\vec m| = |\vec{k}|=F_{n-2}$. Various arguments based on previous works and in particular on ref. \cite{Chamizo:2016msz}, indicate that this choice of twist avoids the breakdown of volume independence in the large $N$ limit. These solutions become relevant on a Hamiltonian formulation of the gauge theory, where they represent vacuum-to-vacuum tunneling events lifting the degeneracy between electric flux sectors present in perturbation theory. We discuss the large $N$ scaling properties of the solutions and evaluate various gauge invariant quantities like the action density or Wilson and Polyakov loop operators.
