22-24 May 2023
Europe/Madrid timezone

State dependence of Krylov complexity in 2d CFT

23 May 2023, 12:00


Arnab Kundu


We compute the Krylov Complexity of a light operator O_L in an eigenstate of a 2d CFT at large central charge. The eigenstate corresponds to a primary operator O_H under the state-operator correspondence. We observe that the behaviour of K-complexity is different (either bounded or exponential) depending on whether the scaling dimension of O_H is below or above the critical dimension h_H=c/24, marked by the 1st order Hawking-Page phase transition point in the dual AdS_3 geometry. Based on this feature, we hypothesize that the notions of operator growth and K-complexity for primary operators in 2d CFTs are closely related to the underlying entanglement structure of the state in which they are computed, thereby demonstrating explicitly their state-dependent nature. To provide further evidence for our hypothesis, we perform an analogous computation of K-complexity in a model of free massless scalar field theory in 2d, and in the integrable 2d Ising CFT, where there is no such transition in the spectrum of states. We will also offer brief comments on ongoing works based on the above study.

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