Complexity measures from geometric actions on Virasoro and Kac-Moody orbits

Understand

We further advance the study of the notion of computational complexity for 2d CFTs based on a gate set built out of conformal symmetry transformations.

• Previously, it was shown that by choosing a suitable cost function, the resulting complexity functional is equivalent to geometric (group) actions on coadjoint orbits of the Virasoro group, up to a term that originates from the central extension.
• We show that this term can be recovered by modifying the cost function, making the equivalence exact.
• Moreover, we generalize our approach to Kac-Moody symmetry groups, finding again an exact equivalence between complexity functionals and geometric actions.