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Probing evaporating black holes with modular flow in SYK

Nicolò Bragagnolo Orcid Logo, Prem Kumar Orcid Logo

Journal of High Energy Physics, Volume: 2026, Issue: 6

Swansea University Author: Prem Kumar Orcid Logo

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DOI (Published version): 10.1007/jhep06(2026)185

Abstract

We study the effect of modular flow on correlation functions of fermions in theSachdev-Ye-Kitaev (SYK) model coupled weakly to a bath, which we take to be another SYKmodel. The system and bath, together are prepared in the thermofield double (TFD) state,and we focus on the effect of modular flow gen...

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Published in: Journal of High Energy Physics
ISSN: 1029-8479
Published: Springer Science and Business Media LLC 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa72118
Abstract: We study the effect of modular flow on correlation functions of fermions in theSachdev-Ye-Kitaev (SYK) model coupled weakly to a bath, which we take to be another SYKmodel. The system and bath, together are prepared in the thermofield double (TFD) state,and we focus on the effect of modular flow generated by the reduced density matrix for theSYK system, obtained by tracing out the bath. We show, in the late time limit, that modularflowed correlators of two Majorana fermions, single-sided and two-sided, exhibit non-trivialsingularities. Beyond a critical value of the modular parameter, the “modular scramblingtime”, the singularity structure shows correlations being transferred from one boundary tothe other. The calculations are performed by employing the replica trick in Euclidean timeand appropriately analytically continuing to real time. Exploiting the connection betweenmodular flow generators and SL(2,ℝ) boosts we use the microscopic picture to reconstructthe dual bulk modular flow in two-sided AdS2 black hole spacetime. Fixed points of the flowallow to identify quantum extremal surfaces (QES) demarcating the entanglement wedge ofthe boundary system and the island. We show that bulk modular flow can move fermioninsertions near the right boundary past the horizon leading to lightcone singularities inappropriately smeared boundary correlators, probing physics beyond the horizon.
College: Faculty of Science and Engineering
Issue: 6

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