Complexity from Spinning Primaries

Understand

We define circuits given by unitary representations of Lorentzian conformal field theory in 3 and 4 dimensions.

• Our circuits start from a spinning primary state, allowing us to generalize formulas for the circuit complexity obtained from circuits starting from scalar primary states.
• These results are nicely reproduced in terms of the geometry of coadjoint orbits of the conformal group.
• In contrast to the complexity geometry obtained from scalar primary states, the geometry is more complicated and the existence of conjugate points, signaling the saturation of complexity, remains open.