Driven inhomogeneous CFT as a theory in curved space-time
Abstract
For two-dimensional conformal field theories driven by evolving background space-time metrics in a closed universe, we present an operator formulation as a driven inhomogeneous CFT. The Hamiltonian of this theory is given by a background space-time dependent smearing of the stress tensor over the spatial slice. Emphasis is placed on the treatment of the curved-space Weyl anomaly, which we show is realized by the difference between Schr\"odinger and Heisenberg picture Hamiltonians once an appropriate renormalization scheme, the chirally split scheme, is chosen. As a result, the unitary evolution generated by the background metric coincides with that of a Virasoro quantum circuit. To showcase our formalism, we consider the stress tensor one-point function and the entanglement entropy of an interval in both operator and curved-space formulations. We find that these curved-space observables admit a state interpretation only in the chirally split scheme. Finally, we derive the holographic dual of the driven CFT in three-dimensional gravity, extending previous works to arbitrary driving. The holographic dictionary reproduces the stress tensor one-point function and the entanglement entropy in a diffeomorphism invariant scheme.
Cite
@article{arxiv.2508.18350,
title = {Driven inhomogeneous CFT as a theory in curved space-time},
author = {Johanna Erdmenger and Jani Kastikainen and Tim Schuhmann},
journal= {arXiv preprint arXiv:2508.18350},
year = {2025}
}
Comments
75 pages, 6 appendices, 1 figure, V2: corrected the answer to Q2 of page 19, corrected an error in the stress tensor 1-point function, corrected signs in diffeomorphism Ward identities, added three new references and other small clarifications