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Operator growth in 2d CFT
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We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing the oscillator realization of the Virasoro algebra and CFT states, we systematically implement the Lanczos algorithm and evaluate the Krylov complexity of simple operators (primaries and the stress tensor) under a unitary evolution protocol. Evolution of primary operators proceeds as a flow into the 'bath of descendants' of the Verma module. These descendants are labeled by integer partitions and have a one-to-one map to Young diagrams. This relationship allows us to rigorously formulate operator growth as paths spreading along the Young's lattice. We extract quantitative features of these paths and also identify the one that saturates the conjectured upper bound on operator growth.
Forward citations
Cited by 3 Pith papers
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Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity
In the brickwall model of a BTZ black hole, hand-tuned Gaussian randomness at a stretched horizon reproduces random-matrix-theory spectral statistics and Krylov complexity peaks for scalar and fermionic probes.
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Reducing a graph walk to distance-layers reproduces Krylov/spread complexity, yielding analytic finite-q SYK Lanczos coefficients and hypercube complexity D sin²(t/D), with faster saturation than classical-walk circuits.
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