Driven inhomogeneous CFT as a theory in curved space-time
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| Format: | Preprint |
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2025
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| _version_ | 1866908608596279296 |
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| author | Erdmenger, Johanna Kastikainen, Jani Schuhmann, Tim |
| author_facet | Erdmenger, Johanna Kastikainen, Jani Schuhmann, Tim |
| contents | 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 Schrödinger 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_18350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Driven inhomogeneous CFT as a theory in curved space-time Erdmenger, Johanna Kastikainen, Jani Schuhmann, Tim High Energy Physics - Theory Quantum Physics 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 Schrödinger 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. |
| title | Driven inhomogeneous CFT as a theory in curved space-time |
| topic | High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2508.18350 |