Operator growth in 2d CFT

A bstract We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing oscillator realization Virasoro algebra CFT states, we systematically implement Lanczos algorithm evaluate Krylov complexity simple operators (primaries stress tensor) under a unitary evolution protocol. Evolution primary proceeds as flow into ‘bath descendants’ Verma module. These descendants are labeled by integer partitions have one-to-one map to Young diagrams. This relationship allows us rigorously formulate paths spreading along Young’s lattice. extract quantitative features these also identify one that saturates conjectured upper bound on growth.