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<p>Using recent developments in expressing one-loop partition functions in Euclidean <i>AdS</i><sub>2</sub> space-times in terms of character integrals, we relate the one-loop effective action for a free field theory in <i>AdS</i><sub>2</sub> (comprised of a massless scalar field and a massless Majorana fermion field) to the partition function of the de Alfaro-Fubini-Furlan (DFF) conformal quantum mechanics (CQM) models on the two global <i>AdS</i><sub>2</sub> boundaries. The equal number of bosonic and fermionic degrees in the field theory guarantee that the one-loop calculation is free of all UV divergences except a logarithmic one consistent with the expected entanglement entropy behaviour in a CQM. Via a thermofield double representation, we compute the entanglement entropy between two copies of the <i>CFT</i><sub>1</sub> (CQM), each living near one of the two boundaries of global <i>AdS</i><sub>2</sub>, in a state at global time <i>τ</i> → – ∞. This entanglement entropy is expressed in terms of the logarithm of the regularised length of a closed particle trajectory infinitesimally near the rim of the Euclidean <i>AdS</i><sub>2</sub> disc. We view this relation between boundary quantum entanglement and a bulk geometrical quantity as the <i>AdS</i><sub>2</sub>/<i>CFT</i><sub>1</sub> version of the Ryu-Takayanagi conjecture in our setup. The boundary entanglement entropy is equal to 4 times the thermodynamic entropy read off from the regularised one-loop effective action in <i>AdS</i><sub>2</sub>. Further, we compute the bulk entanglement entropy associated with black hole horizons in Lorentzian <i>AdS</i><sub>2</sub> and show that it precisely matches the boundary entanglement entropy.</p>

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Bulk-boundary entanglement correspondence and the Ryu-Takayanagi conjecture in an AdS2/CFT1 setup

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  • 发表日期：

    2025年6月19日

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  • Gabriel Lopes Cardoso,
  • Bernardo Moniz Martins,
  • Suresh Nampuri

摘要

Using recent developments in expressing one-loop partition functions in Euclidean AdS2 space-times in terms of character integrals, we relate the one-loop effective action for a free field theory in AdS2 (comprised of a massless scalar field and a massless Majorana fermion field) to the partition function of the de Alfaro-Fubini-Furlan (DFF) conformal quantum mechanics (CQM) models on the two global AdS2 boundaries. The equal number of bosonic and fermionic degrees in the field theory guarantee that the one-loop calculation is free of all UV divergences except a logarithmic one consistent with the expected entanglement entropy behaviour in a CQM. Via a thermofield double representation, we compute the entanglement entropy between two copies of the CFT1 (CQM), each living near one of the two boundaries of global AdS2, in a state at global time τ → – ∞. This entanglement entropy is expressed in terms of the logarithm of the regularised length of a closed particle trajectory infinitesimally near the rim of the Euclidean AdS2 disc. We view this relation between boundary quantum entanglement and a bulk geometrical quantity as the AdS2/CFT1 version of the Ryu-Takayanagi conjecture in our setup. The boundary entanglement entropy is equal to 4 times the thermodynamic entropy read off from the regularised one-loop effective action in AdS2. Further, we compute the bulk entanglement entropy associated with black hole horizons in Lorentzian AdS2 and show that it precisely matches the boundary entanglement entropy.