Complexity for superconformal primaries from BCH techniques

A bstract We extend existing results for the Nielsen complexity of scalar primaries and spinning in four dimensions by including supersymmetry. Specifically, we study circuits that transform a superconformal primary with definite scaling dimension, spin R-charge means continuous unitary gates from $$ \mathfrak{su} su (2 , 2 | \mathcal{N} N ) group. Our analysis makes profitable use Baker-Campbell-Hausdorff formulas special class BCH conjecture motivate. With this approach are able to determine super-Kähler potential characterizing circuit geometry obtain explicit expressions case = 1