论文标题
BCH技术的超符合初选的复杂性
Complexity for superconformal primaries from BCH techniques
论文作者
论文摘要
通过包括超对称性，我们扩展了标量原始的尼尔森复杂性和在四个维度上旋转的原始结果的现有结果。具体而言，我们研究了通过从$ \ Mathbf {\ Mathbf {\ Mathfrak {\ Mathfrak {su}}（2,2,2 | \ Mathcal {n}）$组中的连续统一门来转化具有明确缩放维度的缩放尺寸，自旋和R-Charge的尼尔森复杂性。我们的分析使您可以利用Baker-Campbell-Hausdorff公式，包括我们猜想和激励的特殊类别的BCH公式。通过这种方法，我们能够确定表征电路复杂性几何形状的超级kähler电位，并在$ \ mathcal {n} = 1 $和$ \ mathcal {n} = 2 $ superSymmetrymemmetrys的情况下获得明确的表达式。
We extend existing results for the Nielsen complexity of scalar primaries and spinning primaries in four dimensions by including supersymmetry. Specifically, we study the Nielsen complexity of circuits that transform a superconformal primary with definite scaling dimension, spin and R-charge by means of continuous unitary gates from the $\mathbf{\mathfrak{su}}(2,2|\mathcal{N})$ group. Our analysis makes profitable use of Baker-Campbell-Hausdorff formulas including a special class of BCH formulas we conjecture and motivate. With this approach we are able to determine the super-Kähler potential characterizing the circuit complexity geometry and obtain explicit expressions in the case of $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetry.
