Year: 2022
Type: article
Abstract: 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 $$ \mathfrak{su} $$ su (2, 2| $$ \mathcal{N} $$ 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 $$ \mathcal{N} $$ N = 1 and $$ \mathcal{N} $$ N = 2 supersymmetry.
Source: Journal of High Energy Physics
Authors: Phumudzo Rabambi, Hendrik J. R. van Zyl
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4309636079