Driven inhomogeneous CFT as a theory in curved space-time

• URL: http://arxiv.org/abs/2508.18350v2
• Date: Fri, 24 Oct 2025 09:52:10 GMT
• Title: Driven inhomogeneous CFT as a theory in curved space-time
• Authors: Johanna Erdmenger, Jani Kastikainen, Tim Schuhmann,
• Abstract summary: We present an operator formulation as a driven inhomogeneous CFT.<n>The unitary evolution generated by the background metric coincides with that of a Virasoro quantum circuit.<n>We derive the holographic dual of the driven CFT in three-dimensional gravity.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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