Driven inhomogeneous CFT as a theory in curved space-time

TL;DR

This paper develops a formalism for driven inhomogeneous conformal field theories in curved space-time, analyzing their operator structure, anomalies, and holographic duals, with applications to stress tensor and entanglement entropy calculations.

Contribution

It introduces an operator formulation for driven inhomogeneous CFTs in curved space, including a novel treatment of the Weyl anomaly and holographic duals for arbitrary driving.

Findings

Weyl anomaly is realized by Hamiltonian differences in a specific renormalization scheme.

Curved-space observables like stress tensor and entanglement entropy have a state interpretation only in the chirally split scheme.

Holographic duals reproduce key observables in a diffeomorphism invariant manner.

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.